Question

which expression is equal to $\frac{6}{sqrt{5}}$?
$\frac{36}{sqrt{30}}$
$\frac{6sqrt{5}}{25}$
$\frac{6sqrt{5}}{5}$
$\frac{30}{sqrt{5}}$

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{5}$: $\frac{6}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}$.

Step2: Simplify the expression

$\frac{6\times\sqrt{5}}{\sqrt{5}\times\sqrt{5}}=\frac{6\sqrt{5}}{5}$.

Answer:

$\frac{6\sqrt{5}}{5}$ (the third option)