Answer
$\frac{3 \sqrt 10}{5}$
Work Step by Step
$\frac{3 \sqrt 6}{\sqrt 15}$
To simplify this, we cannot have a radical in the denominator.
We multiply $\frac{3 \sqrt 6}{\sqrt 15}$ by $\frac{ \sqrt 15}{ \sqrt 15}$
$\frac{3 \sqrt 6}{\sqrt 15} \times \frac{ \sqrt 15}{ \sqrt 15}$
$\frac{3 \sqrt 90}{2 \sqrt 15^{2}}$
The factors of 90 is 9 x 10
$\frac{3 \sqrt 9 \sqrt 10}{\sqrt 15^{2}}$
Square root of 9 is 3 because 3 x 3 = 9
Square root of $15^{2}$ is 15 because 15 x 15 = $15^{2}$
$\frac{3 \times 3 \sqrt 10}{15}$
$\frac{9 \sqrt 10}{15}$
$9 \div 15$ can also be written as $3 \div 5$
$\frac{3 \sqrt 10}{5}$
