Question

How do you find the square root $27$?

Answer 1

Find the square root using prime factorization method:

The prime factors of $27$ are

$27=3\times 3\times 3$

Therefore the square root of $27$ is

$\begin{array}{rcl}27& =& 3\times 3\times 3\\ & \Rightarrow & \sqrt{27}=\sqrt{3\times 3\times 3}\\ & \Rightarrow & \sqrt{27}=3\sqrt{3}\end{array}$

$\therefore$The square root of $27$ is $3\sqrt{3}$

Hence, the square root of $\mathbf{27}$ is $\mathbf{3}\sqrt{\mathbf{3}}$.