Find the square root of 135 in radical form

We have to find the square root of 135 in radical form

Solution

We will use prime factorisation method to find the square root

The number 135 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 135.

The first step is to divide the number 135 with the smallest prime factor, say 2.
135 ÷ 3 = 45

Again, when you divide 135 by 3, you will get a fractional number and it cannot be a factor and continue with the next prime factor, say 3
45 ÷ 3 = 15

15÷ 3 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further.

So, the prime factors of 135 are written as 3×3×3×5

On paring the factors we get

135= (3 x 3 ) (5 x 3)

√135= 3 √15

Answer

The square root of 135 = 3 √15

√135= 3 √15

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