Question

Find $\sqrt{324}$ using prime factorization method.

Answer 1

Compute the required value.

Using prime factor we can write that

$324=2\times 2\times 3\times 3\times 3\times 3$

That is

$$\begin{gathered} \sqrt{324}=\sqrt{2\times 2\times 3\times 3\times 3\times 3} \\ =\sqrt{{\left(2\right)}^2{\left(3\right)}^4} \end{gathered}$$

$$\begin{gathered} =2\times 3^2 \\ =2\times 9 \\ =18 \end{gathered}$$ [ removing square and square roots ]

Hence, the value of $\sqrt{324}$ is $18$.