Question

Find the square root of the following number by the prime factorisation method.
$1\frac{17}{64}$

Answer 1

The given number $1\frac{17}{64}$ can be simplified as $\frac{81}{64}$.

The factors of $81$ is $3\times 3\times 3\times 3$ and the factors of $64$ is $2\times 2\times 2\times 2\times 2\times 2$. Therefore,

$\frac{81}{64}=\frac{3\times 3\times 3\times 3}{2\times 2\times 2\times 2\times 2\times 2}$

Taking square root both sides,

$\sqrt{\frac{81}{64}}=\sqrt{\frac{3\times 3\times 3\times 3}{2\times 2\times 2\times 2\times 2\times 2}}$

$=\sqrt{\frac{3^4}{2^6}}$

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

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

$=\frac{9}{8}$

Therefore, the square root of $1\frac{17}{64}$ is $\frac{9}{8}$