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Square Root of 36

Last Updated : 23 Jul, 2025

Square Root 36 is 6. Square Root of 36 is the number that, when multiplied by itself gives back 36 as the result. This means when 6 is multiplied by 6, the product is equal to 36. There are two possible square roots of 36, they are +6 and -6.

In this article, we will discuss what is the square of the root 36, how to represent and how to find it using different methods.

👁 Square-Root-of-36

What is the Square Root of 36?

Square Root of 36, is denoted as √36 and it's equal to 6. So, the original number is '6' when multiplied by itself i.e. 6 × 6 then we get the number 36. Square Root of 36 is represented as follows:

  • Square Root of 36 in Radical Form: √36 = 6
  • Square Root of 36 in Fractional Exponent Form: (36)1/2 = 6

Square Root of 36 Calculator

Try out the following calculator to find the square root of 36

How to Calculate a Square Root of 36?

Some of the methods are given below to find out the square root of 36.

Square Root of 36 by Repeated Subtraction Method

To find the square root of 36 using repeated subtraction method we need to subtract 81 successively by consecutive odd numbers. The number of steps in which the difference becomes zero is the square root of 36. Let's see the process:

  • 36 - 1 = 35
  • 35 - 3 = 32
  • 32 - 5 = 27
  • 27 - 7 = 20
  • 20 - 9 = 11
  • 11 - 11 = 0

Here, the difference is zero in the 6th step. Hence, the square root of 36 is 6.

Square Root 36 by Prime Factorization Method

Square root of 36 can be found easily using the following steps;

  • Step 1: Break down 36 into prime factors. Hence, √36 = 2 × 2 × 3 × 3
  • Step 2: Now, Take one factor from each pair and multiply them together: √36 ​= √(2 × 2) × (3 × 3)
  • Step 3: Then after combining the factors, √36 ​= √(2 × 3​)2
  • Step 4: After multiplying the numbers under square root will be √36 ​= 6
  • So, the square root of 36 is 6 by using the prime factorization method.

The prime factorization of 36 is shown below:

👁 Prime-Factorization-of-36

Is Square Root of 36 Rational or Irrational?

Square root of 36 is rational. Since the square root of 36 is 6 it can be represented as a straightforward fraction in the form of p/q. Hence, the square root of 36 is a rational number.

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