Question

Find the root of $400$ by the Prime Factorisation Method

Answer 1

Find the square root by prime factorisation method:

Given number, $400$

Factorisation,

$\therefore 400=2\times 2\times 2\times 2\times 5\times 5$

So, the square root of $400$ is

$$\begin{gathered} 400=2\times 2\times 2\times 2\times 5\times 5 \\ \Rightarrow \sqrt{400}=\sqrt{2\times 2\times 2\times 2\times 5\times 5} \\ \Rightarrow \sqrt{400}=2\times 2\times 5 \\ \therefore \sqrt{400}=20 \end{gathered}$$

Hence, the square root of $400$ is $20$.