Rationalize (frac{2sqrt{3} + 3 sqrt{2}}{3sqrt{2} – 2 sqrt{3}})
-
A.
5 – 2(sqrt{6}) -
B.
5 + 2(sqrt{6}) -
C.
5(sqrt{6}) -
D.
5
Correct Answer: Option B
Explanation
(frac{2sqrt{3} + 3 sqrt{2}}{3sqrt{2} – 2 sqrt{3}})
= (frac{2sqrt{3} + 3 sqrt{2}}{3sqrt{2} – 2 sqrt{3}}) x (frac{3sqrt{2} + 2 sqrt{3}}{3sqrt{2} – 2 sqrt{3}})
(frac{4(3) + 9(2) + 2(6) sqrt{6}}{9(2) – 4(3)})
(frac{12 + 18 + 12sqrt{6}}{1`8 – 12})
= (frac{30 + 12sqrt{6}}{6})
= 5 + 2(sqrt{6})