If \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}\) is simplified as m + n\(\sqrt{6}\), find the value of (m + n)

A.

\(\frac{1}{3}\)

B.

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

C.

1\(\frac{1}{3}\)

D.

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

Correct answer is C

\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}\) = \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)

= \(\frac{\sqrt{2} \times \sqrt{3} + \sqrt{3} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}\)

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

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

= Hence, (m + n) = 1 + \(\frac{1}{3}\)


= 1\(\frac{1}{3}\)