How do you simplify the square root of 162?

We have to find the square root of 162

Solution

To find the square root of 162 we will factorise it first

Prime factorisation of 162

Here we have to find the prime factors of 162.

Divide 162 by 2;

162 ÷ 2 = 81

Divide 81 by 3

81 ÷ 3 = 27

Divide 27 by 3

27 ÷ 3 = 9

Divide 9 by 3

9 ÷ 3 = 3

Then divide 3 by 3

3 ÷ 3 = 1

So the prime factorisation of 162 is

162 = 2 X 3 X 3 X 3 X 3

Now we know the values of √3, √5 and √7 we get

On paring the factors we get

162 = 2 X (3 X 3) X(3 X 3)

√162= √2 X (3 X 3) X(3 X 3)

√162= 3 x 3 x √2

√162= 9√2

Answer

Hence The square root of 162 is 9√2

Hence, √162 = 9√2