Rationalize (frac{5sqrt{7} – 7sqrt{5}}{sqrt{7} – sqrt{5}})
-
A.
-2 sqrt{35}) -
B.
4sqrt{7}) – 6(sqrt{5}) -
C.
-(sqrt{35}) -
D.
4sqrt{7}) – 8(sqrt{5}) -
E.
(sqrt{35})
Correct Answer: Option C
Explanation
(frac{5sqrt{7} – 7sqrt{5}}{sqrt{7} – sqrt{5}}) = (frac{5sqrt{7} – 7sqrt{5}}{sqrt{7} – sqrt{5}}) x (frac{sqrt{7} + sqrt{5}}{sqrt{7} + sqrt{5}})
= (frac{(5 times 7) + (5 sqrt{7} times 5) – (7 times sqrt{5} times 7) (-7 times 5)}{(sqrt{7})^2})
= (frac{5 sqrt{35} – 7sqrt{35}}{2})
= (frac{-2sqrt{35}}{2})
= – (sqrt{35})