Express (frac{8 – 3sqrt{6}}{2sqrt{3} + 3sqrt{2}}) in the form (psqrt{3} + qsqrt{2}).
-
A.
(7sqrt{3} – frac{17sqrt{2}}{3}) -
B.
(7sqrt{2} – frac{17sqrt{3}}{3}) -
C.
(-7sqrt{2} + frac{17sqrt{3}}{3}) -
D.
(-7sqrt{3} – frac{17sqrt{2}}{3})
Correct Answer: Option B
Explanation
Given (frac{8 – 3sqrt{6}}{2sqrt{3} + 3sqrt{2}}),
first, we rationalise by multiplying through with (2sqrt{3} – 3sqrt{2}) (the inverse of the denominator).
((frac{8 – 3sqrt{6}}{2sqrt{3} + 3sqrt{2}})(frac{2sqrt{3} – 3sqrt{2}}{2sqrt{3} – 3sqrt{2}}))
= (frac{16sqrt{3} – 24sqrt{2} – 18sqrt{2} + 18sqrt{3}}{4(3) – 6sqrt{6} + 6sqrt{6} – 9(2)})
= (frac{34sqrt{3} – 42sqrt{2}}{-6} = 7sqrt{2} – frac{17sqrt{3}}{3})