What is $$\frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2\sqrt {20} - \sqrt {32} + \sqrt {50} }}$$ equal to ?
A. 5
B. $$5\sqrt 2 $$
C. $$5\sqrt 5 $$
D. $$\sqrt 5 $$
Answer: Option D
Solution (By Examveda Team)
$$\eqalign{ & {\text{Given,}} \cr & \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2\sqrt {20} - \sqrt {32} + \sqrt {50} }}{\text{ }} \cr & = \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2 \times 2\sqrt 5 - 2 \times 2\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 4\sqrt 5 - 4\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{5 + \sqrt {10} }}{{\sqrt 5 + \sqrt 2 }} \cr & = \frac{{\sqrt 5 \left( {\sqrt 5 + \sqrt 2 } \right)}}{{\sqrt 5 + \sqrt 2 }} \cr & = \sqrt 5 \cr} $$This Question Belongs to Arithmetic Ability >> Square Root And Cube Root
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