Question

How do you find the square root $33$?

Answer 1

Find the square root:

Given number, $33$

The prime factors of $33$ are

$33=11\times 3$

Therefore the square root of $33$ is

$\begin{array}{rcl}33& =& 3\times 11\\ & \Rightarrow & \sqrt{33}=\sqrt{3\times 11}\\ & \Rightarrow & \sqrt{33}=\sqrt{11}\times \sqrt{3}\\ & \Rightarrow & \sqrt{33}=\left(3.316\right)·\left(1.732\right)\left[\because \sqrt{11}=3.316\mathrm{and}\sqrt{3}=1.732\right]\\ & \Rightarrow & \sqrt{33}=5.744\\ & & \end{array}$

Hence, the square root of $\mathbf{33}$ is $\mathbf{5}\mathbf{.}\mathbf{744}$.