Question

Find the square root of the following.
$156.25$

Answer 1

Simplifying $\sqrt{156.25}$.

$\sqrt{156.25}=\sqrt{\frac{15625}{100}}$

The factors of 15625 is $5\times 5\times 5\times 5\times 5\times 5$ and the factors of $100$ are $2\times 2\times 5\times 5$.

$\sqrt{\frac{15625}{100}}=\sqrt{\frac{5\times 5\times 5\times 5\times 5\times 5}{2\times 2\times 5\times 5}}$

$=\sqrt{\frac{5^6}{2^2\times 5^2}}$

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

$=\frac{125}{10}$

$=12.5$

Therefore, the square root of $156.25$ is $12.5$.