How do you simplify sqrt(27/a^2)?

Feb 27, 2017

$= \frac{3 \sqrt{3}}{a}$

Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

You are looking for squared values. They can be 'taken outside' the root.

You can write: $\sqrt{\frac{27}{a} ^ 2} \text{ as } \frac{\sqrt{27}}{\sqrt{{a}^{2}}}$

If you are ever unsure of something try it out using easy numbers
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

Write as:$\text{ } \frac{\sqrt{27}}{\sqrt{{a}^{2}}} = \frac{\sqrt{27}}{a}$

Known that $3 \times 9 = 27 = 3 \times {3}^{2}$

Write as:$\text{ } \frac{\sqrt{3 \times {3}^{2}}}{a} = \frac{3 \sqrt{3}}{a}$