Evaluate the square root of 128 in radical form

We have to find the square root of 128 in radical form

Solution

We will use prime factorisation method to find the square root

√128 =

The first step is to divide the number 128 with the smallest prime factor, say 2.
128 ÷ 2 = 64

Again divide 64 by 2
64÷ 2 = 32

Again divide 32 by 2

32 ÷ 2 = 16

Again divide 16 by 2

16 ÷ 2 = 8

Again divide 8 by 2

8 ÷ 2 = 4

Again divide 4 by 2

4÷ 2 = 2

Again divide 2 by 2

2÷ 2 = 1

On combining factors we get

128 = 2×2×2×2×2×2×2

√128 = √(2 x 2 x 2 x 2 x 2 x 2 x 2)

On paring

√128 = √ (2 x 2 ) (2×2) (2 x 2) (2)

√128 = 8 √2

Answer

The square root of 128 = 8 √2

√128=8 √2

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