Express (frac{2}{3 – sqrt{7}} text{ in the form} a + sqrt{b}), where a and b are integers.
-
A.
(6 + sqrt{7}) -
B.
(3 + sqrt{7}) -
C.
(3 – sqrt{7}) -
D.
(6 – sqrt{7})
Correct Answer: Option B
Explanation
Rationalizing (frac{2}{3 – sqrt{7}}) by multiplying through with (3 + sqrt{7}),
(frac{2}{3 – sqrt{7}} frac{(3 + sqrt{7})}{(3 + sqrt{7})} = frac{6 + 2sqrt{7}}{9 – 7})
= (frac{6 + 2sqrt{7}}{2} = 3 + sqrt{7})