Rationalize ( frac{2sqrt{3}} + sqrt{5} sqrt{5} – sqrt{3} )
-
A.
3√15 – 11 -
B.
(frac{3sqrt {15} – 11}{2}) -
C.
3√15 + 11 -
D.
(frac{3sqrt {15} + 11}{2})
Correct Answer: Option D
Explanation
(frac{2sqrt{3}} + sqrt{5}}{sqrt{5} – sqrt{3}) = (frac{sqrt{5}} + 2sqrt{3}}{sqrt{5} – sqrt{3}) x (frac{sqrt{5}} + sqrt{3}}{sqrt{5} + sqrt{3})
(frac{5 + sqrt{15} + 2sqrt{15} + 2 times 3}{(sqrt{5} – sqrt{3})^2)
= (frac{5 + 3sqrt{15} +6} {5 – 3))
= (frac{11 + 3sqrt{15}}{2})