Question

How do you find the square root $500$?

Answer 1

Find the square root using prime factorization method:

Given number, $500$

The prime factors of $500$ are

$500=5\times 5\times 5\times 2\times 2\left[\because 500÷2=250,250÷2=125,125÷5=25,25÷5=5,5÷5=1\right]$

Therefore the square root of $500$ is

$\begin{array}{rcl}500& =& 5\times 5\times 5\times 2\times 2\\ & \Rightarrow & \sqrt{500}=\sqrt{5\times 5\times 5\times 2\times 2}\\ & \Rightarrow & \sqrt{500}=5\times 2\times \sqrt{5}\\ & \Rightarrow & \sqrt{500}=10\sqrt{5}\end{array}$

Hence, the square root of $\mathbf{500}$ is $\mathbf{10}\sqrt{\mathbf{5}}$.