Question

How do you find the square root $2000$?

Answer 1

Find the square root using prime factorization method:

The prime factors of $2000$ are

$2000=2\times 2\times 2\times 2\times 5\times 5\times 5$

Therefore the square root of $2000$ is

$\begin{array}{rcl}2000& =& 2\times 2\times 2\times 2\times 5\times 5\times 5\\ & \Rightarrow & \sqrt{2000}=\sqrt{2\times 2\times 2\times 2\times 5\times 5\times 5}\\ & \Rightarrow & \sqrt{2000}=2\times 2\times 5\times \sqrt{5}\\ & \Rightarrow & \sqrt{2000}=20\sqrt{5}\end{array}$

Hence, the square root of $\mathbf{2000}$ is $\mathbf{20}\sqrt{\mathbf{5}}$.