Question

Evaluate the square root of $128$ in the radical form

Answer 1

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

Step 1

Prime factorizing given number

The first step is to divide the number $128$ with the smallest prime factor, say $2$ and then by other factors till we get $1$

$$\begin{gathered} 128÷2=64 \\ 64÷2=32 \\ 32÷2=16 \\ 16÷2=8 \\ 8÷2=4 \\ 4÷2=2 \\ 2÷2=1 \end{gathered}$$

So

$128=2\times 2\times 2\times 2\times 2\times 2\times 2$

Step 2

Finding square root by pairing the factors

$$\begin{gathered} \Rightarrow \sqrt{128}=\sqrt{(2\times 2)\times (2\times 2)\times (2\times 2)\times 2} \\ \Rightarrow \sqrt{128}=2\times 2\times 2\sqrt{2} \\ \Rightarrow \sqrt{128}=8\sqrt{2} \end{gathered}$$

Hence, the square root of $128$ is $8\sqrt{2}$