Question

The value of $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$is

• A. $\sqrt{5}(5 + \sqrt{2})$
• B. $\sqrt{5}(2 + \sqrt{2})$
• C. $\sqrt{5}(1 + \sqrt{2})$
• D. $\sqrt{5}(3 + \sqrt{2})$

Answer 1

Answer: (C)

$\sqrt{5}(1 + \sqrt{2})$

Answer 2

Given fraction

$= \frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} = \frac{15}{\sqrt{10} + 2\sqrt{5} + 2\sqrt{10} - \sqrt{5} - 4\sqrt{5}} = \frac{15}{3\sqrt{10} - 3\sqrt{5}} = \frac{5}{\sqrt{10} - \sqrt{5}}.\frac{\sqrt{10} + \sqrt{5}}{\sqrt{10} + \sqrt{5}}$

=$\sqrt{10} + \sqrt{5} = \sqrt{5}(\sqrt{2} + 1)$