Question

express in simplest form with a rational denominator.\\(\frac{5}{\sqrt{27}}\\)

Explanation:

Step1: Simplify the radical denominator

$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$, so $\frac{5}{\sqrt{27}} = \frac{5}{3\sqrt{3}}$

Step2: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{3}$:
$\frac{5 \times \sqrt{3}}{3\sqrt{3} \times \sqrt{3}} = \frac{5\sqrt{3}}{3 \times 3}$

Step3: Simplify the denominator

$\frac{5\sqrt{3}}{9}$

Answer:

$\frac{5\sqrt{3}}{9}$