how to find square root math problem

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Education and Communications
Mathematics

How to Solve Square Root Problems

Last Updated: March 7, 2023 References

This article was co-authored by David Jia . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. There are 11 references cited in this article, which can be found at the bottom of the page. This article has been viewed 335,002 times.

While the intimidating sight of a square root symbol may make the mathematically-challenged cringe, square root problems are not as hard to solve as they may first seem. Simple square root problems can often be solved as easily as basic multiplication and division problems. More complex square root problems, on the other hand, can require some work, but with the right approach, even these can be easy. Start practicing square root problems today to learn this radical new math skill!

Understanding Squares and Square Roots

Try squaring a few more numbers on your own to test this concept out. Remember, squaring a number is just multiplying it by itself. You can even do this for negative numbers. If you do, the answer will always be positive. For example, (-8) 2 = -8 × -8 = 64 .

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On the other hand, numbers that don't give whole numbers when you take their square roots are called imperfect squares . When you take one of these numbers' square roots, you usually get a decimal or fraction. Sometimes, the decimals involved can be quite messy. For instance, √(13) = 3.605551275464...

Image titled Solve Square Root Problems Step 4

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Note that although imaginary numbers can't be represented with ordinary digits, they can still be treated like ordinary numbers in many ways. For instance, the square roots of negative numbers can be squared to give those negative numbers, just like any other square root. For example, i 2 = -1

Using Long Division-Style Algorithms

Image titled Solve Square Root Problems Step 7

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In our example, we would divide 6.45 into pairs like this: 6-.45-00 . Note that there is a "leftover" digit on the left — this is OK.

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In our example, the first group in 6-.45-00 is 6. The biggest number that is less than or equal to 6 when squared is 2 — 2 2 = 4. Write a "2" above the 6 under the radical.

Image titled Solve Square Root Problems Step 10

In our example, we would start by taking the double of 2, the first digit of our answer. 2 × 2 = 4. Next, we would subtract 4 from 6 (our first "group"), getting 2 as our answer. Next, we would drop down the next group (45) to get 245. Finally, we would write 4 once more to the left, leaving a small space to add onto the end, like this: 4_.

Image titled Solve Square Root Problems Step 11

In our example, we want to find the number to fill in the blank in 4_ × _ that makes the answer as large as possible but still less than or equal to 245. In this case, the answer is 5 . 45 × 5 = 225, while 46 × 6 = 276.

Image titled Solve Square Root Problems Step 12

Continuing from our example, we would subtract 225 from 245 to get 20. Next, we would drop down the next pair of digits, 00, to make 2000. Doubling the numbers above the radical sign, we get 25 × 2 = 50. Solving for the blank in 50_ × _ =/< 2,000, we get 3 . At this point, we have "253" above the radical sign — repeating this process once again, we get a 9 as our next digit.

Image titled Solve Square Root Problems Step 13

In our example, the number under the radical sign is 6.45, so we would simply slide the point up and place it between the 2 and 5 digits of our answer, giving us 2.539 .

Quickly Estimating Imperfect Squares

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For example, let's say we need to find the square root of 40. Since we've memorized our perfect squares, we can say that 40 is in between 6 2 and 7 2 , or 36 and 49. Since 40 is greater than 6 2 , its square root will be greater than 6, and since it is less than 7 2 , its square root will be less than 7. 40 is a little closer to 36 than it is to 49, so the answer will probably be a little closer to 6. In the next few steps, we'll narrow our answer down.

Image titled Solve Square Root Problems Step 15

In our example problem, a reasonable estimate for the square root of 40 might be 6.4 , since we know from above that the answer is probably a little closer to 6 than it is to 7.

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In our example, let's pick 6.33 for our two-decimal point estimate. Multiply 6.33 by itself to get 6.33 × 6.33 = 40.0689. Since this is slightly above our original number, we'll try a slightly lower number, like 6.32. 6.32 × 6.32 = 39.9424. This is slightly below our original number, so we know that the exact square root is between 6.33 and 6.32 . If we wanted to continue, we would keep using this same approach to get an answer that's continually more and more accurate.

Calculator, Practice Problems, and Answers

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For quick solutions, use a calculator. Most modern calculators can instantly find square roots. Usually, all you need to do is to simply type in your number, then press the button with the square root symbol. To find the square root of 841, for example, you might press: 8, 4, 1, (√) and get an answer of 29 . [16] X Research source ⧼thumbs_response⧽ Helpful 0 Not Helpful 0

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About This Article

To solve square root problems, understand that you are finding the number that, when multiplied by itself, equals the number in the square root. For quick recall, memorize the first 10-12 perfect squares, so that you recognize the square root of numbers like 9, 25, 49, or 121. If possible, break the number under the square root into individual perfect squares. For example, √(900) can be broken into √(9) × √(100), and √(100) can be broken into √(25) × √(4), reducing the problem to √(9) × √(25) × √(4), or 3 x 5 x 2 for an answer of 30. If you want to learn how to estimate imperfect square roots, keep reading the article! Did this summary help you? Yes No

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Square Root

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number. If 'a' is the square root of 'b', it means that a × a = b. The square of any number is always a positive number, so every number has two square roots, one of a positive value, and one of a negative value. For example, both 2 and -2 are square roots of 4. However, in most places, only the positive value is written as the square root of a number.

What is Square Root?

The square root of a number is that factor of a number which when multiplied by itself gives the original number. Squares and square roots are special exponents . Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 3 2 . Here, the exponent is 2, and we call it a square. Now when the exponent is 1/2, it refers to the square root of the number. For example, √n = n 1/2 , where n is a positive integer.

Square Root Definition

The square root of a number is the value of power 1/2 of that number. In other words, it is the number whose product by itself gives the original number. It is represented using the symbol '√ '. The square root symbol is called a radical , whereas the number under the square root symbol is called the radicand.

How to Find Square Root?

It is very easy to find the square root of a number that is a perfect square. Perfect squares are those positive numbers that can be expressed as the product of a number by itself. in other words, perfect squares are numbers which are expressed as the value of power 2 of any integer . We can use four methods to find the square root of numbers and those methods are as follows:

Repeated Subtraction Method of Square Root

Square root by prime factorization method, square root by estimation method, square root by long division method.

It should be noted that the first three methods can be conveniently used for perfect squares, while the fourth method, i.e., the long division method can be used for any number whether it is a perfect square or not.

This is a very simple method. We subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach 0. The number of times we subtract is the square root of the given number. This method works only for perfect square numbers. Let us find the square root of 16 using this method.

16 - 1 = 15

You can observe that we have subtracted 4 times. Thus,√16 = 4

Prime factorization of any number means to represent that number as a product of prime numbers . To find the square root of a given number through the prime factorization method, we follow the steps given below:

Let us find the square root of 144 by this method.

This method works when the given number is a perfect square number.

Estimation and approximation refer to a reasonable guess of the actual value to make calculations easier and more realistic. This method helps in estimating and approximating the square root of a given number. Let us use this method to find √15. Find the nearest perfect square numbers to 15. 9 and 16 are the perfect square numbers nearest to 15. We know that √16 = 4 and √9 = 3. This implies that √15 lies between 3 and 4. Now, we need to see if √15 is closer to 3 or 4. Let us consider 3.5 and 4. Since 3.5 2 = 12.25 and 4 2 = 16. Thus, √15 lies between 3.5 and 4 and is closer to 4.

Let us find the squares of 3.8 and 3.9. Since 3.8 2 = 14.44 and 3.9 2 = 15.21. This implies that √15 lies between 3.8 and 3.9. We can repeat the process and check between 3.85 and 3.9. We can observe that √15 = 3.872.

This is a very long process and time-consuming.

Long Division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. We can find the exact square root of any given number using this method. Let us understand the process of finding square root by the long division method with an example. Let us find the square root of 180.

Step 3: Bring down the number under the next bar to the right of the remainder . Add the last digit of the quotient to the divisor . To the right of the obtained sum, find a suitable number which, together with the result of the sum, forms a new divisor for the new dividend that is carried down.

Step 4: The new number in the quotient will have the same number as selected in the divisor. The condition is the same — as being either less than or equal to the dividend.

Step 5: Now, we will continue this process further using a decimal point and adding zeros in pairs to the remainder.

Step 6: The quotient thus obtained will be the square root of the number. Here, the square root of 18 0 is approximately equal to 13.4 and more digits after the decimal point can be obtained by repeating the same process as follows.

Square Root Table

The square root table consists of numbers and their square roots. It is useful to find the squares of numbers as well. Here is the list of square roots of perfect square numbers and some non-perfect square numbers from 1 to 10.

The square roots of numbers that are not perfect squares are irrational numbers .

Square Root Formula

The square root of a number has the exponent of 1/2. The square root formula is used to find the square root of a number. We know the exponent formula: $\sqrt[\text{n}]{x}$ = x 1/n . When n= 2, we call it square root. We can use any of the above methods for finding the square root, such as prime factorization, long division, and so on. 9 1/2 = √9 = √(3×3) = 3. So, the formula for writing the square root of a number is √x= x 1/2 .

How to Simplify Square Root?

To simplify a square root, we need to find the prime factorization of the given number. If a factor cannot be grouped, retain them under the square root symbol. The rule of simplifying square root is √xy = √(x × y), where, x and y are positive integers. For example: √12 = $\sqrt{2 \times 2\times3}$ = 2√3

For fractions, there is also a similar rule: √x/√y = √(x/y). For example: √50/√10 = √(50/10)= √5

Square Root of a Negative Number

The square root of a negative number cannot be a real number, since a square is either a positive number or zero. But complex numbers have the solutions to the square root of a negative number. The principal square root of -x is: √(-x)= i√x. Here, i is the square root of -1.

For example: Take a perfect square number like 16. Now, let's see the square root of -16. There is no real square root of -16. √(-16)= √16 × √(-1) = 4i (as, √(-1)= i), where 'i' is represented as the square root of -1. So, 4i is a square root of -16.

Square of a Number

Any number raised to exponent two (y 2 ) is called the square of the base. So, 5 2 or 25 is referred to as the square of 5, while 8 2 or 64 is referred to as the square of 8. We can easily find the square of a number by multiplying the number two times. For example, 5 2 = 5 × 5 = 25, and 8 2 = 8 × 8 = 64. When we find the square of a whole number, the resultant number is a perfect square. Some of the perfect squares we have are 4, 9, 16, 25, 36, 49, 64, and so on. The square of a number is always a positive number.

How to Find the Square of a Number?

The square of a number can be found by multiplying a number by itself. For single-digit numbers, we can use multiplication tables to find the square, while in the case of two or more than two-digit numbers, we perform multiplication of the number by itself to get the answer. For example, 9 × 9 = 81, where 81 is the square of 9. Similarly, 3 × 3 = 9, where 9 is the square of 3.

The square of a number is written by raising the exponent to 2. For example, the square of 3 is written as 3 2 and is read as "3 squared". Here are some examples:

Squares and Square Roots

There is very strong relation between squares and square roots as each one of them is the inverse relation of the other. i.e., if x 2 = y then x = √y. It can be simply remembered like this:

This logic helps in solving many equations in algebra. Consider the following example:

Example: Solve the equation √(2x + 3) = 10.

Squaring on both sides of the equation would result in the cancellation of the square root on the left side.

Square Root of Numbers

Examples on square root.

Example 1: Find out the square root of 529 by the prime factorization method.

Prime factorization of 529 .

We can see that, 529 = 23×23 ⇒ √529= 23

∴ √529= 23.

Answer: 23

Example 2: Find the square and square root of the following numbers. a) Square root of 25 is ___ b) Square of 16 is ____ c) Square of 20 is ____ d) Square root of 400 is _____

a) Square root of 25 is 5 5 × 5 = 25 √25 = 5 b) Square of 16 is = 16 × 16 = 256 c) Square of 20 is = 20 × 20 = 400 d) Square root of 400 is 20 as 20 × 20 = 400 √400 = 20.

Answer: a) 5 b) 256 c) 400 d) 20

Example 3: Determine the square root of 60.

To find: square root of 60

From prime factorization of 60 , we get,

60 = 2 × 2 × 3 × 5

= (2) 2 × 3 × 5

Using square root formula,

√60 = [(2) 2 × 15 ] 1/ 2

√60 = 2√15

Therefore, Square root of 60 = 2√15

Answer: 2√15

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Practice Questions on Square Root

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FAQs on Square Root

What is square root in math.

The square root of a number is a number that when multiplied by itself gives the actual number. For example, 2 is the square root of 4, and this is expressed as √4 = 2. This means when 2 is multiplied by 2 it results in 4 and this can be verified as 2 × 2 = 4.

How to Find the Square Root of a Number?

It is very easy to find the square root of a number that is a perfect square . For example, 9 is a perfect square, 9 = 3 × 3. So, 3 is the square root of 9 and this can be expressed as √9 = 3. The square root of any number, in general, can be found by using any of the four methods given below:

How to Find the Square Root of a Decimal Number?

The square root of a decimal number can be found by using the estimation method or the long division method. In the case of decimal numbers, we make pairs of whole number parts and fractional parts separately. And then, we carry out the process of long division in the same way as any other whole number.

Can Square Root be Negative?

Yes, the square root of a number can be negative. In fact, all the perfect squares like 4, 9, 25, 36, etc have two square roots, one is a positive value and one is a negative value. For example, the square roots of 4 are -2 and 2. To verify this, we can see that (-2) × (-2) = 4. Similarly, the square roots of 9 are 3 and -3.

What is the Square Root Symbol?

The symbol that is used to denote square root is called the radical sign '√ '. The term written inside the radical sign is called the radicand.

What is the Formula for Calculating the Square Root of a Number?

The square root of any number can be expressed using the formula: √y = y ½ . In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.

What is the Square and Square Root of a Number?

The square of a number is the product that we get on multiplying a number by itself. For example, 6 × 6 = 36. Here, 36 is the square of 6. The square root of a number is that factor of the number and when it is multiplied by itself the result is the original number. Now, if we want to find the square root of 36, that is, √36, we get the answer as, √36 = 6. Hence, we can see that the square and the square root of a number are inverse operations of each other.

Which Method is Used to Find the Square Root of Non-Perfect Square Numbers?

In Math, a non-perfect or an imperfect square number is considered as a number whose square root cannot be found as an integer or as a fraction of integers. The square root of a non-perfect square number can be calculated by using the long division method.

How to Find a Square Root on a Calculator?

To find the square root value of any number on a calculator, we simply need to type the number for which we want the square root and then insert the square root symbol √ in the calculator. For example, if we need to find the square root of 81, we should type 81 in the calculator and then press the symbol √ to get its square root. We will get √81 = 9.

How to Multiply Two Square Root Values Together?

Let us say we have two numbers a and b. First, we will find the square root of the numbers a and b. Then, after finding the square root we will multiply the square roots value together. Let us understand this with a practical illustration. For example, multiply √4 × √16. The square root of 4 is 2 (√4 = 2) and the square root of 16 is 4 (√16 = 4). Now, we will multiply the value of the square root of 4 and 16, i.e., 2 × 4 = 8. Instead, we can apply the property of square roots, √a × √b = √ab.

What are the Applications of the Square Root Formula?

There are various applications of the square root formula:

What does the Square of a Number mean?

The product that we get on multiplying a number by itself is the square of the number. For example, 5 × 5 = 25. Here, 25 is the square of 5 and this can also be written as 5 2 = 25.

How to Find the Square Root of a Negative Number?

Note that the square root of a negative number is not a real number . It is an imaginary number . For example, √(-4) = √(-1) × √4 = i (2) = 2i, where 'i' is known as " iota " and i 2 = -1 (or) i = √(-1).

Why is the Square of a Negative Number Positive?

The square of a negative number is positive because when two negative numbers are multiplied it always results in a positive number. For example, (-4) × (-4) = 16.

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Unit 11: Lesson 3

Simplifying square roots.

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The Basics of Square Roots (Examples & Answers)

How to Solve a Square Root Equation

Square roots are often found in math and science problems, and any student needs to pick up the basics of square roots to tackle these questions. Square roots ask “what number, when multiplied by itself, gives the following result,” and as such working them out requires you to think about numbers in a slightly different way. However, you can easily understand the rules of square roots and answer any questions involving them, whether they require direct calculation or just simplification.

TL;DR (Too Long; Didn't Read)

A square root asks you which number, when multiplied by itself, gives the result after the √ symbol. So √9 = 3 and √16 = 4. Every root technically has a positive and a negative answer, but in most cases the positive answer is the one you’ll be interested in.

You can factor square roots just like ordinary numbers, so √ ab = √ a √ b , or √6 = √2√3.

Square roots are the opposite of “squaring” a number, or multiplying it by itself. For example, three squared is nine (3 2 = 9), so the square root of nine is three. In symbols, this is

The “√” symbol tells you to take the square root of a number, and you can find this on most calculators.

Remember that every number actually has two square roots. Three multiplied by three equals nine, but negative three multiplied by negative three also equals nine, so

with the ± standing in for “plus or minus.” In many cases, you can ignore the negative square roots of numbers, but sometimes it’s important to remember that every number has two roots.

You may be asked to take the “cube root” or “fourth root” of a number. The cube root is the number that, when multiplied by itself twice, equals the original number. The fourth root is the number that when multiplied by itself three times equals the original number. Like square roots, these are just the opposite of taking the power of numbers. So, 3 3 = 27, and that means the cube root of 27 is 3, or

The “∛” symbol represents the cube root of the number that comes after it. Roots are sometimes also expressed as fractional powers, so

One of the most challenging tasks you may have to perform with square roots is simplifying large square roots, but you just need to follow some simple rules to tackle these questions. You can factor square roots in the same way as you factor ordinary numbers. So for example 6 = 2 × 3, so

Simplifying larger roots means taking the factorization step by step and remembering the definition of a square root. For example, √132 is a big root, and it might be hard to see what to do. However, you can easily see it’s divisible by 2, so you can write

However, 66 is also divisible by 2, so you can write:

In this case, a square root of a number multiplied by another square root just gives the original number (because of the definition of square root), so

In short, you can simplify square roots using the following rules

Using the definitions and rules above, you can find the square roots of most numbers. Here are some examples to consider.

The square root of 8

This can’t be found directly because it isn’t the square root of a whole number. However, using the rules for simplification gives:

The square root of 4

This makes use of the simple square root of 4, which is √4 = 2. The problem can be solved exactly using a calculator, and √8 = 2.8284....

The square root of 12

Using the same approach, try to work out the square root of 12. Split the root into factors, and then see if you can split it into factors again. Attempt this as a practice problem, and then look at the solution below:

Again, this simplified expression can either be used in problems as needed, or calculated exactly using a calculator. A calculator shows that

The square root of 20

The square root of 20 can be found in the same way:

The square root of 32

Finally, tackle the square root of 32 using the same approach:

Here, note that we already calculated the square root of 8 as 2√2, and that √4 = 2, so:

Although the definition of a square root means that negative numbers shouldn’t have a square root (because any number multiplied by itself gives a positive number as a result), mathematicians encountered them as part of problems in algebra and devised a solution. The “imaginary” number i is used to mean “the square root of minus 1” and any other negative roots are expressed as multiples of i . So

These problems are more challenging, but you can learn to solve them based on the definition of i and the standard rules for roots.

Test your understanding of square roots by simplifying as needed and then calculating the following roots:

Try to solve these before looking at the answers below:

How to use pemdas & solve with order of operations..., how to factor with negative fractional exponents, how to solve cubic equations, algebra rules for beginners, the four types of multiplication properties, what are addends in math addition problems, how to find the square root of a number, definition of successor and predecessor in math, the difference between scientific & engineering notation, what are radicals in math, how to divide exponents with different bases, how to write the prime factorization in exponent form, how to divide negative numbers, quotient rule for exponents, how to factor polynomials with 4 terms, how to simplify exponents, how to explain division to a third grader, how to factor monomials, how to find cube root in ti-84.

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Lee Johnson is a freelance writer and science enthusiast, with a passion for distilling complex concepts into simple, digestible language. He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. He was also a science blogger for Elements Behavioral Health's blog network for five years. He studied physics at the Open University and graduated in 2018.

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How to Use PEMDAS & Solve With Order of Operations (Examples)

How to find the square root of a number and calculate it by hand

At times, in everyday situations, we may face the task of having to figure the square root of a number. What if there is no calculator or a smartphone handy? Can we use an old fashioned paper and pencil to do it in a long division style?

Yes we can, and there are several different methods. Some are more complex than others. Some provide more accurate results.

The one I want to share with you is one of them. To make this article more reader friendly, each step comes with illustrations.

STEP 1: Separate The Digits Into Pairs

To begin, let's organize the workspace. We will divide the space into three parts. Then, let’s separate the number’s digits into pairs moving from right to left.

For example, the number 7,469.17 becomes 74 69. 17 . Or in the case of a number with an odd amount of digits such as 19,036, we will start with 1 90 36 .

In our case here, 2,025 becomes 20 25 .

STEP 2: Find The Largest Integer

As the next step, we need to find the largest integer (i) whose square is less than or equal to the leftmost number.

In our current example the leftmost number is 20. Since 4² = 16 <= 20 and 5² = 25 > 20, the integer in question is 4. Let’s deposit 4 to the top-right corner and 4² = 16 to the bottom right one.

STEP 3: Now Subtract That Integer

Now we need to subtract the square of that integer (which equals 16) from the leftmost number (which equals 20). The result equals 4 and we will write it as shown above.

STEP 4: Let's Move To The Next Pair

Next, let's move down the next pair in our number (which is 25). We write it next to the subtracted value already there (which is 4).

Now multiply the number in the top right corner (which is also 4) by 2. This results in 8 and we write it in the bottom right corner followed by _ x _ =

STEP 5: Find The Right Match

Time to fill in each blank space with the same integer (i). It must be the largest possible integer that allows the product to be less than or equal the number on the left.

For example, if we choose the number 6, the first number becomes 86 (8 and 6) and we must also multiply it by 6. The result 516 is greater than 425, so we go lower and try 5. The number 8 and the number 5 give us 85. 85 times 5 results in 425, which is exactly what we need.

Write 5 next to 4 in the top right corner. It is the second digit in the root.

STEP 6: Subtract Again

Subtract the product we calculated (which is 425) from the current number on the left (also 425). The result is zero, which means the task is complete.

Note: I chose a perfect square (2025 = 45 x 45) on purpose. This way I could show the rules for solving square root problems.

In reality, numbers consist of many digits, including the ones after the decimal point. In that case we repeat steps 4, 5 and 6 until we reach any accuracy we want.

The next example explains what I mean.

EXAMPLE: We dig deeper...

This time the number consists of an odd number of digits including the ones after the decimal point.

As we saw in this example, the process can repeat several times over to reach a desired level of accuracy.

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Simplifying Square Roots

To simplify a square root: make the number inside the square root as small as possible (but still a whole number ):

Example: √12 is simpler as 2√3

Get your calculator and check if you want: they are both the same value!

Here is the rule: when a and b are not negative

And here is how to use it:

Example: simplify √12

12 is 4 times 3:

Use the rule:

And the square root of 4 is 2:

So √12 is simpler as 2√3

Another example:

Example: simplify √8

(Because the square root of 4 is 2)

And another:

Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2

It often helps to factor the numbers (into prime numbers is best):

Example: simplify √6 × √15

First we can combine the two numbers:

Then we factor them:

Then we see two 3s, and decide to "pull them out":

There is a similar rule for fractions:

Example: simplify √30 / √10

Then simplify:

Some Harder Examples

Example: simplify √20 × √5 √2.

See if you can follow the steps:

Example: simplify 2√12 + 9√3

First simplify 2√12:

Now both terms have √3, we can add them:

Note: a root we can't simplify further is called a Surd . So √3 is a surd. But √4 = 2 is not a surd.

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IMAGES

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VIDEO

Solving Square Root Equations
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FIND THE VALUE OF X

COMMENTS

What Is the History of the Square Root in Mathematics?
According to Saint Louis University, the ancient Egyptians created the square root and most likely used it for architecture, building pyramids and other daily activities that required math. Most of the present-day knowledge of Egyptian math...
What Are Real Roots in Math?
In algebra, a real root is a solution to a particular equation. The term real root means that this solution is a number that can be whole, positive, negative, rational, or irrational.
What Is the Square Root of 17?
The square root of 17 is approximately 4.12. Since 17 is a prime number, it cannot be rewritten in simplified radical form. The square root of 17 can be found by using the radical sign function on both scientific and graphing calculators.
How to Solve Square Root Problems (with Pictures)
Square a number by multiplying it by itself. To understand square roots, it's best to start with squares. Squares are easy—taking the square of a number is just
How To Simplify Square Roots
This math video tutorial explains how to simplify square roots.My E-Book: https://amzn.to/3B9c08zVideo Playlists: https://www.video-tutor.
How To Calculate Square Roots In Your Head
There's an incredible method to extract the square root of a perfect square in your head.MIT Entrace Exam Arithmetic 1876
Formula, Examples
First, we will find the square root of the numbers a and b. Then, after finding the square root we will multiply the square roots value together. Let us
Solving square-root equations: one solution (video)
So let me explain. Let's assume x is positive. x^2=x*x , of course. But -x*-x=x^2. You can try this with any number. Let's say x^2=y. So the square root of y
Simplifying square roots
Roots are nice, but we prefer dealing with regular numbers as much as possible. So, for example, instead of √4 we prefer dealing with 2.
The Basics of Square Roots (Examples & Answers)
The “√” symbol tells you to take the square root of a number, and you can find this on most calculators.
How to find the square root of a number and calculate it by hand
STEP 1: Separate The Digits Into Pairs · STEP 2: Find The Largest Integer · STEP 3: Now Subtract That Integer · STEP 4: Let's Move To The Next Pair.
Squares and Square Roots
A Fun Way to Calculate a Square Root ; a) start with a guess (let's guess 4 is the square root of 10) ; around, b) divide by the guess (10/4 = 2.5) c) add that to
Simplifying Square Roots
Simplifying Square Roots · Example: √12 is simpler as 2√3. Get your calculator and check if you want: they are both the same value! · Example: simplify √12. 12
Free square root worksheets (PDF and html)
If you want the answer to be a whole number, choose "perfect squares," which makes the radicand to be a perfect square (1, 4, 9, 16, 25, etc.). If you choose to