Find the square root of 484

Square root of a number is the value that returns the original number on multiplied by itself. Finding square root by prime factorisation is an easy method. We need to factories the number under the root and pair them in two.

Finding the square root of 484

We will find the square root of 484 by prime factorisation method

The prime factorisation of 484 can be written as:

The first step is to divide the number 484 with the smallest prime factor, i.e. 2.
484 ÷ 2 = 242

Now, dividing 242 by 2 we get,
242 ÷ 2 = 121

Now, dividing 121 by 11 we get,

121 ÷ 11 =11

Now, dividing 11 by 11 we get,

11÷ 11 = 1

We have received 1 at the end and further, we cannot proceed with the division method, as we know the multiple of 1 is 1 only.

So, the prime factors of 484 are 2 x 2 x 11 x 11

On paring to find square root we get

Square root of 484 = √484= √(2X 2 X 11 x 11)

= √484= (2 x 11)

√484= 22

Answer

Hence, the square root of 484 = √484=22

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