Square root of 100
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Last updated on August 5, 2025

The square root of 100 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 100. The number 100 has a unique non-negative square root, called the principal square root.

What Is the Square Root of 100?

The square root of 100 is ±10, where 10 is the positive solution of the equation

 x2 = 100. Finding the square root is just the inverse of squaring a number and hence, squaring 10 will result in 100. 

The square root of 100 is written as √100 in radical form, where the ‘√’  sign is called the  “radical” sign. In exponential form, it is written as (100)1/2 

Finding the Square Root of 100

We can find the square root of 100 through various methods. They are:

i) Prime factorization method

ii) Long division method

iii) Repeated subtraction method

Square Root of 100 By Prime Factorization Method

The prime factorization of 100 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore. After factorizing 100, make pairs out of the factors to get the square root.

So, Prime factorization of 100 = 2 × 5 ×2 × 5

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Square Root of 100 By Long Division Method

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 100:

 Step 1: Write the number 100 and draw a bar above the pair of digits from right to left.

 Step 2: Now, find the greatest number whose square is less than or equal to 1. Here, it is 1 because 12=1.

Step 3: Now divide 1 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  Double the divisor 1, we get 2, and then the largest possible number A1=0 is chosen such that when 0 is written beside the new divisor 2, a 2-digit number is formed →20, and multiplying 0 with 20 gives 0, which is less than or equal to 0. Repeat this process until you reach the remainder of 0. 

 Step 4: The quotient obtained is the square root of 100. In this case, it is 10.

Square Root of 100 By Subtraction Method

We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be a count of the number of steps required to obtain 0. Here are the steps:

Step 1: take the number 100 and then subtract the first odd number from it. Here, in this case, it is 100-1=99

Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from step 1), i.e., 99, and again subtract the next odd number after 1, from 3, i.e., 99-3=96. Like this, we have to proceed further.

Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 10 steps. So, the square root is equal to the count, i.e., the square root of 100 is ±10.

Common Mistakes and How to Avoid Them in the Square Root of 100

When we find the square root of 100, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.

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Problem 1

Find the radius of a circle whose area is 100π² cm².

Okay, lets begin

    Given, the area of the circle = 100π cm2

           Now, area = πr2 (r is the radius of the circle)

           So, 

        πr2 = 100π cm2

        We get, r2 = 100 cm2

        r = √100 cm

        Putting the value of √100 in the above equation, 

        We get, r = ±10 cm

        Here we will consider the positive value of 10.

        Therefore, the radius of the circle is 10 cm.

Answer: 10cm.

Explanation

We know that, area of a circle = πr2 (r is the radius of the circle). According to this equation, we are getting the value of “r” as 10 cm by finding the value of the square root of 100.

Well explained 👍

Problem 2

Find the length of a side of a square whose area is 100 cm²

Okay, lets begin

 Given, the area = 100 cm2

           We know that, (side of a square)2 = area of square

                              Or,  (side of a square)2 = 100

                               Or,  (side of a square)= √100

                            Or, the side of a square = ± 10.

         But, the length of a square is a positive quantity only, so, the length of the side is

       10 cm.

Answer: 10 cm

Explanation

We know that, (side of a square)2 = area of square. Here, we are given with the l area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square. 

Well explained 👍

Problem 3

Simplify the expression: √100 ╳ √100, √100+√100

Okay, lets begin

 √100 ╳ √100

                     =  √(10 ╳ 10)    ╳    √(10 ╳ 10)

                       =  10 ╳ 10

                       =  100

                      √100+√100

                      = √(10 ╳ 10)  + √(10 ╳ 10) 

                        = 10 + 10

                        = 20

Answer: 100, 20

Explanation

 In the first expression, we multiplied the value of the square root of 100 with itself. In the second expression, we added the value of the square root of 100 with itself.

Well explained 👍

Problem 4

If y=√100, find y²

Okay, lets begin

Firstly, y=√100= 10

                     Now, squaring y, we get, 

                   y2=102=100

                  or, y2=100

Answer : 100

Explanation

Squaring “y” which is same as squaring the value of √100 resulted to 100.

Well explained 👍

Problem 5

Calculate (√100/5 + √100/2)

Okay, lets begin

√100/5 + √100/2

                     = 10/5 + 10/2

                     = 2 + 5

                     = 7

 Answer : 7

Explanation

From the given expression, we first found the value of square root of 100 then solved by simple divisions and then simple addition. 

Well explained 👍

FAQs on 100 Square Root

1.Is 100 a rational number?

2.Is 100 a perfect square or a non-perfect square?

100 is a perfect square, since 100 =10 2.

3.Is the square root of 100 a rational or irrational number?

The square root of 100 is ±10. So, 10 is a rational number since it can be obtained by dividing two integers and can be written in the form 10/1. 

4.How to write square root of 100?

The square root of 100 is written as √100 in radical form.

5.How is the square root of 100 used in real life?

The square root of 100 can be used in real-life applications, like in geometry, to determine the side length of a square with an area of 100 sq units.

6.How does the square root of 100 compare to the square root of other numbers?

  •  √100 = ±10
  •  √25 = ±5
  •  √16 =± 4

The square root of a perfect square is always an integer

7.What is the square root of 100 in decimal form?

 The square root of 100 in decimal form is 10.

Important Glossaries for Square Root of 100

1)Exponential form

An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.

Ex: 2 ⤬ 2 ⤬ 2 ⤬ 2 = 16

Or, 2 4 = 16, where 2 is the base, 4 is the exponent 

2)Factorization   

Expressing the given expression as a product of its factors

Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3

3) Prime Numbers 

Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

4)  Rational numbers and Irrational numbers

The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

5)  perfect and non-perfect square numbers

Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24                       

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