Question

Find the square root of the following number by the prime factorisation method.
$5625$

Answer 1

The factors of $5625$ is,

$5625=5\times 5\times 5\times 5\times 3\times 3$

Take square root both sides,

$\sqrt{5625}=\sqrt{5\times 5\times 5\times 5\times 3\times 3}$

$=\sqrt{5^4\times 3^2}$

$=\sqrt{{\left({\left(5\right)}^2\times 3\right)}^2}$

$=25\times 3$

$=75$

Therefore, the square root of 5625 is 75.