Question

Find the root of $4096$ by the Prime Factorisation Method

Answer 1

Find the square root by prime factorisation method

Given number, $4096$

Factorisation,

$\therefore 4096=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

So, the square root of $4096$ is

$$\begin{gathered} 4096=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2 \\ \Rightarrow \sqrt{4096}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2} \\ \Rightarrow \sqrt{4096}=2\times 2\times 2\times 2\times 2\times 2 \\ \therefore \sqrt{4096}=64 \end{gathered}$$

Hence, the square root of $4096$ is $64$.