Rationalize the expression (frac{1}{sqrt{2} + sqrt{5}})
-
A.
(frac{1}{3})((sqrt{5} – sqrt{2}) -
B.
(frac{sqrt{2}}{3}) + (frac{sqrt{5}}{5}) -
C.
(sqrt{2} – sqrt{5}) -
D.
5((sqrt{2} – sqrt{5}) -
E.
(frac{1}{3})((sqrt{2} – sqrt{5})
Correct Answer: Option A
Explanation
(frac{1}{sqrt{2} + sqrt{5}})
(frac{1}{sqrt{2} + sqrt{5}} times frac{(sqrt{2} – sqrt{5})}{(sqrt{2} – sqrt{5})})
= (frac{sqrt{2} – sqrt{5}}{2 – 5})
= (frac{sqrt{2} – sqrt{5}}{-3})
= (frac{1}{3} (sqrt{5} – sqrt{2}))