Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)

A.

\(3\sqrt{2}\)

B.

\(5\sqrt{2}\)

C.

\(\frac{5\sqrt{2}}{2}\)

D.

\(\frac{3\sqrt{2}}{2}\)

Correct answer is C

\(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}} = \frac{\sqrt{3} + 4\sqrt{3}}{\sqrt{6}}\)

\(\frac{5\sqrt{3}}{\sqrt{6} = \frac{5\sqrt{3} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}}\)

\(\frac{5\sqrt{18}{6} = \frac{15\sqrt{2}}{6}\)

= \(\frac{5\sqrt{2}}{2}\)