Square Root of 100

Last Updated : 13 Feb, 2024

Square Root of 100 is 10. 100 is a perfect square number, as it can be written as 10 × 10 = 100. The square root is represented by √ for radical form, and we can also represent it using 0.5 or 1/2 as exponents. Thus, √100, (100)^0.5, and (100)^1/2 all represent the value of the square root of 100. In this article, we will discuss the value of the square root of 100 as well as all the methods to find that value.

Square-Root-of-100

Square Root Definition

The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, for a non-negative real number n, the square root of n is denoted as n, and it satisfies the equation √(n)²= n.

For example:

The square root of 9 is 3, because 3 × 3 = 9.
The square root of 16 is 4, because 4 × 4 = 16.

What is the Square Root of 100?

The square root of 100 is 10

This is because 10 × 10 = 10² = 100. Square root of any number can be positive and negative i.e., 10 and –10.

Square Root Calculator

How to Calculate a Square Root of 100?

Some of the methods are given below to find out the square root of 100.

Square Root 100 by Prime Factorization Method
Square Root 100 by Repeated Subtraction Method

Square Root 100 by Prime Factorization Method

Let’s derive the square root of 100 in the following steps by using the prime factorization method;

Step 1: Break down the prime Factorization of 100, which can be expressed as 2 × 2 × 5 × 5 or 2² × 5²

Prime-Factorization-of-100

Step 2: Now, we pair up the prime factors in twos because we’re finding the square root. i.e.;2 × 5.
Step 3: That gives us 2 × 5 = 10.
Step 4: Therefore, the square root of 100 is 10.

Square Root 100 by Repeated Subtraction Method

The square root can be found by repeatedly subtracting odd numbers from the provided number until it equals zero. This process is known as repeated subtraction. So, In this process number of odd numbers we subtract here will be treated as a square root of 100;

100-1 = 99
99-3 = 96
96-5 = 91
91-7 = 84
84-9 = 75
75-11 = 64
64-13 = 51
51-15 = 36
36-17 = 19
19-19 = 0

Therefore, The square root of 100 is 10 because we have started from 100 and subtracted with odd numbers,10 times to obtain 0.

Is Square Root of 100 Rational or Irrational?

100 is a rational square root. We check to see if the integer under the square root sign (the radicand) is a perfect square to establish whether a square root is rational or irrational. So, here 2²× 5² is the prime factorization of 100 and 100 is a perfect square because there is a repeated prime factor.

Therefore 100 is a rational number since its square root can be written as a simple fraction.

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