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: Option C
Explanation
(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})