Question

How do you simplify the square root of $162$?

Answer 1

Solve for the required value

The prime factorization of $162$ is

$162=2\times 3\times 3\times 3\times 3$

On paring the factors we get

$$\begin{gathered} 162=2\times (3\times 3)\times (3\times 3) \\ \Rightarrow \sqrt{162}=\sqrt{2\times (3\times 3)\times (3\times 3)} \\ \Rightarrow \sqrt{162}=3\times 3\times \sqrt{2} \\ \Rightarrow \sqrt{162}=9\sqrt{2} \end{gathered}$$,

Hence, the square root of $162$is $9\sqrt{2}$.