Question

Find the square root of the following number by the prime factorisation method.
$6\frac{1}{4}$

Answer 1

The given number $6\frac{1}{4}$ can be simplified as $\frac{25}{4}$.

The factors of 25 is $5\times 5$ and the factors of 4 is $2\times 2$. Therefore,

$\frac{25}{4}=\frac{5\times 5}{2\times 2}$

Taking square root both sides,

$\sqrt{\frac{25}{4}}=\sqrt{\frac{5\times 5}{2\times 2}}$

$=\sqrt{\frac{5^2}{2^2}}$

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

$=\frac{5}{2}$

Therefore, the square root of $6\frac{1}{4}$ is $\frac{5}{2}$.