Question

How do you find the square root $85$?

Answer 1

Find the square root using prime factorization method:

Given number, $85$

The square root of $85$ is

$\begin{array}{rcl}85& =& 5\times 17\\ & \Rightarrow & \sqrt{85}=\sqrt{5\times 17}\\ & \Rightarrow & \sqrt{85}=\sqrt{5}·\sqrt{17}\\ & \Rightarrow & \sqrt{85}=\left(2.236\right)·\left(4.123\right)\left[\because \sqrt{17}=4.123,\sqrt{5}=2.236\right]\\ & \Rightarrow & \sqrt{85}=9.219\end{array}$

Hence, the square root of $\mathbf{85}$ is $\mathbf{9}\mathbf{.}\mathbf{219}$.