Simplify (frac{1 + sqrt{8}}{3 – sqrt{2}}).
-
A.
(7 + sqrt{2}) -
B.
(7 + 7sqrt{2}) -
C.
(1 – 7sqrt{2}) -
D.
(1 + sqrt{2})
Correct Answer: Option D
Explanation
(frac{1 + sqrt{8}}{3 – sqrt{2}})
Rationalizing by multiplying through with (3 + sqrt{2}),
((frac{1 + sqrt{8}}{3 – sqrt{2}})(frac{3 + sqrt{2}}{3 + sqrt{2}}) = frac{3 + sqrt{2} + 3sqrt{8} + 4}{9 – 2})
= (frac{3 + sqrt{2} + 3sqrt{4 times 2} + 4}{7} )
= (frac{7 + 7sqrt{2}}{7} = 1 + sqrt{2})