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

Sep 26, 2016

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

#### Explanation:

Write the values under the root in factor form, trying to make squares where possible.

Find the square roots where you can.

sqrt(27/p^2) = sqrt((3xx9)/p^2) =sqrt(3xx3^2xxp^-2
=$\sqrt{3} \times \sqrt{{3}^{2}} \times \sqrt{{\left({p}^{-} 1\right)}^{2}}$

by mathematical definition
$\sqrt{3} = \sqrt{3}$
$\sqrt{{3}^{2}} = 3$
$\sqrt{{\left({p}^{-} 1\right)}^{2}} = \sqrt{{\left(\frac{1}{p}\right)}^{2}} = \frac{1}{p}$
=$3 \times \frac{1}{p} \sqrt{3}$
$= \frac{3 \sqrt{3}}{p}$