Question

Find the square root of the following number by the prime factorisation method.
$\frac{289}{144}$

Answer 1

The factors of 289 is $17\times 17$ and the factors of 144 is $2\times 2\times 2\times 2\times 3\times 3$. Therefore,

$\frac{289}{144}=\frac{17\times 17}{2\times 2\times 2\times 2\times 3\times 3}$

Taking square root both sides,

$\sqrt{\frac{289}{144}}=\sqrt{\frac{17\times 17}{2\times 2\times 2\times 2\times 3\times 3}}$

$=\sqrt{\frac{{17}^2}{2^4\times 3^2}}$

$=\sqrt{{\left(\frac{17}{2^2\times 3}\right)}^2}$

$=\frac{17}{2^2\times 3}$

$=\frac{17}{12}$

Therefore, the square root of $\frac{289}{144}$ is $\frac{17}{12}$.