Question

Find the root of $729$ by the Prime Factorisation Method.

Answer 1

Find the square root by prime factorisation method:

Given number, $729$

Factorisation,

$\therefore 729=3\times 3\times 3\times 3\times 3\times 3$

So, the square root of $729$ is

$$\begin{gathered} 729=3\times 3\times 3\times 3\times 3\times 3 \\ \Rightarrow \sqrt{729}=\sqrt{3\times 3\times 3\times 3\times 3\times 3} \\ \Rightarrow \sqrt{729}=3\times 3\times 3 \\ \therefore \sqrt{729}=27 \end{gathered}$$

Hence, the square root of $729$ is $27$.