Question

How do you find the square root $324$?

Answer 1

Find the square root using prime factorization method:

The prime factors of $324$ are

$324=2\times 2\times 3\times 3\times 3\times 3324÷2=162,162÷2=81÷3=27,27÷3=9,9÷3=3,3÷3=1$

Therefore the square root of $324$ is

$\begin{array}{rcl}324& =& 2\times 2\times 3\times 3\times 3\times 3\\ & \Rightarrow & \sqrt{324}=\sqrt{2\times 2\times 3\times 3\times 3\times 3}\\ & \Rightarrow & \sqrt{324}=2\times 3\times 3\end{array}$

Hence, the square root of $\mathbf{324}$ is $\mathbf{18}$.