Question

what is the simplest form of the radical expression?\\(\frac{2sqrt{5}}{sqrt{12}}\\)\\(\circ) \\(\frac{sqrt{5}}{3}\\)\\(\circ) \\(\frac{2sqrt{15}}{6}\\)\\(\circ) \\(\frac{sqrt{15}}{3}\\)\\(\circ) \\(sqrt{5}\\)

Explanation:

Step1: Simplify denominator radical

$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

Step2: Substitute simplified denominator

$\frac{2\sqrt{5}}{2\sqrt{3}} = \frac{\sqrt{5}}{\sqrt{3}}$

Step3: Rationalize the denominator

$\frac{\sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{15}}{3}$

Answer:

$\boldsymbol{\frac{\sqrt{15}}{3}}$ (corresponding to the third option)