Question

Find the square root of the following.
$75.69$

Answer 1

$\sqrt{75.69}=\sqrt{\frac{7569}{100}}$

The factors of $7569$ is $3\times 3\times 29\times 29$ and the factors of $100$ is $2\times 2\times 5\times 5$.

So,

$\begin{array}{cc}\sqrt{\frac{7569}{100}}& =\sqrt{\frac{3\times 3\times 29\times 29}{2\times 2\times 5\times 5}}\\ & =\sqrt{\frac{3^2\times {29}^2}{2^2\times 5^2}}\\ & =\sqrt{{\left(\frac{3\times 29}{2\times 5}\right)}^2}\\ & =\frac{87}{10}\\ & =8.7\end{array}$

Therefore, the square root of $75.69$ is $8.7$.