Question

Find the root of $1764$ by the Prime Factorisation Method

Answer 1

Find the square root by prime factorisation method

Given number, $1764$

Factorisation,

$1764=2\times 2\times 3\times 3\times 7\times 7$

So, the square root of $1764$ is

$$\begin{gathered} 1764=2\times 2\times 3\times 3\times 7\times 7 \\ \Rightarrow \sqrt{1764}=\sqrt{2\times 2\times 3\times 3\times 7\times 7} \\ \Rightarrow \sqrt{1764}=2\times 3\times 7 \\ \therefore \sqrt{1764}=42 \end{gathered}$$

Hence, the square root of $1764$ is $42$.