Square root of 36

Square root of 36 is a natural number that results in the original number when multiplied by itself. Thus, the square root of any number is equal to the number that can be squared to get the actual number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.

The square root of 36 is expressed by √36, where ‘√’ is the radical symbol and 36 is the radicand. √36 is equal to 6, which is a rational number. In this article, we can find the square root of the number 36 with the help of different methods.

Also check:

• Find Square Root Of Decimals
• Square Root 1 to 100
• Square Root Of A Number By Repeated Subtraction
• Square Root Tricks

How to Find the Square root of 36?

Square root of 36 is a rational number. Suppose the root of 36 is x, then we can represent it as x/1. Hence, x is the numerator and 1 is the denominator.

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

• Prime Factorisation Method
• Division Method
• Repeated Subtraction Method

Prime Factorisation Method

Prime factorisation method is the simplest method to find the prime factors of a number. After that, we can pair the factors that can be denoted as n², where n is the prime factor. Hence, after taking the square root of the equation on both sides, we can cancel the root with a square.

Let us work on it.

The prime factorisation of 36 is:

36 = 2 x 2 x 3 x 3

The exponential form will be:

36 = 2² x 3²

Or

36 = 2² x 3² [Using laws of exponents: a^m.aⁿ = a^m+n]

Taking square root on both sides of the equation, we get;

Now, we can cancel each of the square roots on the right-hand side of the equation with the square of each term. Therefore, we get;

√36 = 2 x 3

√36 = 6

Therefore, the square root of 36 is 6.

Division Method

We can easily find the square root of a number, using the division method. We need to find such a number that can be multiplied by itself to get 36. Since 36 is itself a smaller two-digit number. Therefore, the required square root value will be a single-digit number.

Let us find here the square root of 36 using the division method.

Therefore, the square root of 36 is equal to 6.

Repeated Subtraction Method

In the repeated subtraction method, we start subtracting 36 with the successive odd numbers in every step till we get the final value equal to 0. The number of times subtraction is done is equal to the square root of the original number.

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

Thus, the number of times subtraction is done is equal to 6. Hence, the required square root is 6.

Square Roots of Numbers

• Square root of 4 = 2
• Square root of 16 = 4
• Square Root of 25 = 5
• Square root of 49 = 7
• Square root of 81 = 9
• Square root of 64 = 8
• Square root of 32 = 5.65685424949
• Square root of 24 = 4.89897948557
• Square root of 100 = 10

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Solved Examples

Q.1: What is the value of 10 multiplied by √36?

Solution: The value of 10 multiplied by √36 is:

⇒ 10 x √36

⇒ 10 x 6

⇒ 60

Hence, the answer is 60.

Q.2: Find the area of a square whose side is equal to 6 cm each.

Solution: Given, the side of the square is 6cm.

As we know,

Area of the square = side²

Area = 6²

Area = 36 sq.cm.

Q.3: If the area of a square-shaped tile is 36 units, then find the perimeter of the tile.

Solution: Given,

Area of the tile = 36 units

Therefore,

Side length of the tile = √area = √36 = 6 unit

Therefore, the perimeter of the tile is;

Perimeter = 4side = 4 x 6 = 24 units.

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