Question

Find the square root of the following number by the prime factorisation method.
$4096$

Answer 1

The factors of $4096$ is,

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

Take square root both sides,

$\sqrt{4096}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}$

$=\sqrt{2^{12}}$

$=\sqrt{{\left({\left(2\right)}^6\right)}^2}$

$=2^6$

$=64$

Therefore, the square root of 4096 is 64.