Question

How do you find the square root $189$?

Answer 1

Find the square root using prime factorization method:

The prime factors of $189$ are

$189=3\times 3\times 3\times 7$

Therefore the square root of $189$ is

$\begin{array}{rcl}189& =& 3\times 3\times 3\times 7\\ & \Rightarrow & \sqrt{189}=\sqrt{3\times 3\times 3\times 7}\\ & \Rightarrow & \sqrt{189}=3\sqrt{21}\end{array}$

Hence, the square root of $\mathbf{189}$ is $\mathbf{3}\sqrt{\mathbf{21}}$.