Question

Find the square root of the following.
$10.0489$

Answer 1

Simplifying $\sqrt{10.0489}$.

$\sqrt{10.0489}=\sqrt{\frac{100489}{10000}}$

The factors of 100489 is $317\times 317$ and the factors of 10000 is $2\times 2\times 2\times 2\times 5\times 5\times 5\times 5$.

So,

$\sqrt{\frac{100489}{10000}}=\sqrt{\frac{{317}^2}{2^4\times 5^4}}$

$=\sqrt{{\left(\frac{317}{2^2\times 5^2}\right)}^2}$

$=\frac{317}{4\times 25}$

$=\frac{317}{100}$

$=3.17$

Therefore, the square root of $10.0489$ is $3.17$.