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Square Root

What Is the Square Root of 36? How to Find the Square Root of 36?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 36? How to Find the Square Root of 36?

What Is the Square Root of 36? How to Find the Square Root of 36?

The square root of 36 is 6. The square root of a number is the value when multiplied by itself gives the original number. The square root for the exponential form is denoted as 361/2 or 360.5 the radical way of writing 8 is expressed as √36. Thus, they give the original number when the number is squared.

The number 36 is a perfect square number that can be easily found. Since the square root of 36 is 6, where 6 is a rational number the square root of 36 can be found by three methods.

Methods to find the square root of 36

There are three methods to find the square root of 36:

  • Prime factorization method
  • Long division method
  • Repeated subtraction method

Prime factorization method

Prime factorization to find the square root is used to find only those numbers that are perfect squares. n is the prime factor. When the prime factors of the number are found the similar factors are squared as n2. After taking a square on both sides the root with a square is canceled. 

  • Step 1: Find the prime factors of the given number
    • Prime factors of 36 =  2 x 2 x 3 x 3
  • Step 2:  Take the similar factors, by multiplying them we get the square root
    • 36 = 2 x 3 = 6

The exponential form can be written as,
36 = 22 x 32.
Next, take square on both sides
√36 = √22x √32
√36 = 2 x 3 = 6
Hence, the square root of √36 = 6.

Long division method

Finding the square root of a perfect square number using the long division method is simple. Since 36 is a small two-digit number the divisor itself is a small single-digit number that can be its square. 

Long division method
Long division method

Hence, √36 = 6.

Repeated subtraction method

The repeated subtraction method first subtracts the given number from the odd numbers until you get zero. The step in which zero is obtained is the square root of the number. It is a time-consuming and lengthy process. 

  1. 36-1 = 35
  2. 35-3 = 32
  3. 32-5 = 27
  4. 27-7 = 20
  5. 20-9 = 11
  6. 11-11 = 0

We got zero in the sixth step. Hence,  √36 = 6.

Solved examples:

Q1: what is the value of 4 when multiplied by 36
A1: The square root of 36 = 6
Therefore, by multiplying 4×6 =24
Hence the value of 4 when multiplied by 36 = 24.

Q2: what is the area of the square whose each side is equal to 6cm
A2: Area of the square = x2
Here x= 6
Therefore, 62 = 6 x 6 = 36
Hence the area of the square with 6cm = 36 sq. cm

Q3: Find the perimeter of the square if the area of the square tile is 36.
A3: The area of the square = 36.
The side length of the tile = √area
Therefore, √36 = 6
A square has 4 sides, by multiplying we get 24.
Therefore the perimeter of the tile = 24 units

Q4: Find the square root of 36 using the law of exponential.
A4: The square root for exponential is replaced by 36 1/2
= (62)1/2 
Therefore, 62 = 36= [6 (am)n. =amn]
√36 = 6

Q5: What is the square root of 36 using the prime factor
A5: 36 =  2 x 2 x 3 x 3
36 = 2 x 3 = 6
√36 = 6

Frequently asked questions

What is the square root of 36?
The √36 = 6

Is 36 a perfect square number?
Yes, 36 is a perfect square number.

What is a rational number?
 A rational number is a real number where the denominator when divided is, pq ≠ 0.

What is the square root of 5?
The square root of 5 = 2.23

What is the square root of 36 using the long division method?

Long division method
Long division method 

√ 36 = 6

What are the methods to find the square root of rational numbers?
There are three methods to find the square root of 36
Prime factorization method
Long division method
Repeated subtraction method

We hope that we have answered all your queries related to the square root of 36!

Written by

Prerit Jain

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