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 it’s 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.

Square root of 36 = √36 = ±6

Or

In Exponent Form,

(36)½ = ±6

Also check:

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

Prime factorisation method is a 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: am.an = am+n]

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

\(\sqrt{36} = \sqrt{2^{2}}\times \sqrt{3^{2}}\)

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.

Facts:

  • Square root of 36 is a natural or a whole number
  • 36 and it’s square root, both are even numbers
  • 36 is a composite number
  • 36 is a perfect square
  • 36 is evenly divisible by its square root value, thus, 6 is the factor of 36
  • The roots of 36 are +6 or -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.

Square root of 36

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

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 6cm, 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.

Practice Questions

  1. √36 + √16 + √49 = ?
  2. √36 divided by 6 is equal to _______.
  3. Is the value of √36 evenly divisible by 10?
  4. What should be subtracted from 9 to get the value of √36?
  5. What should be added to 2 to get the value of √36?

Register with us and download BYJU’S – The Learning App to learn more about squares and square roots with the help of interactive videos.

Frequently Asked Questions on Square root of 36

What is the square root of 36?

The square root of 36 is equal to 6
√36 = 6.

Is 36 a perfect square?

Yes, 36 is a perfect square because the square of the natural number 6, results in the actual number.
62 = 36

What kind of number is the square root of 36?

Square root of 36 is a rational number because it can be expressed in the form of a ratio or p/q.
√36 = 6 = 6/1
Where 6 is the numerator and 1 is the denominator.

Which is the shortcut method to find the square root of 36?

36 is a two digit number, therefore, we can easily realise that any square of any single digit number will result in 36. Since, at the unit place we have 6, so it is clear that when 6 is multiplied by 6, then only we can have 6 at the unit place. Also, if we simply remember the table of 6, we can get 6 x 6 = 36. Therefore, the square root of 36 will be 6.

Why is the square root of 36 equal to 6?

The square root of any number is the root of the number, that is squared to get the original number. Hence, the root of 36 is 6 because when square the number 6, we get the actual number.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class