Question

How do you find the square root $300$?

Answer 1

Find the square root using prime factorization method:

The prime factors of $300$ are

$300=2\times 2\times 5\times 5\times 3$

Therefore the square root of $300$ is

$\begin{array}{rcl}300& =& 2\times 2\times 5\times 5\times 3\\ & \Rightarrow & \sqrt{300}=\sqrt{2\times 2\times 5\times 5\times 3}\\ & \Rightarrow & \sqrt{300}=2\times 5\times \sqrt{3}\\ & \Rightarrow & \sqrt{300}=10\sqrt{3}\end{array}$

Hence, the square root of $\mathbf{300}$ is $\mathbf{10}\sqrt{\mathbf{3}}$.