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Question

Evaluate $${{15} \over {\sqrt {10}  + \sqrt {20}  + \sqrt {40}  - \sqrt 5  - \sqrt {80} }}$$ , it being  given that $$\sqrt 5  = 2.236$$ and $$\sqrt {10}  = 3.162$$


Solution

$$\dfrac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}=\dfrac{15}{\sqrt{10}+2\sqrt{5}+2\sqrt{10}-\sqrt{5}-4\sqrt{5}}=\dfrac{15}{3\sqrt{10}-3\sqrt{5}}$$
                                                             $$=\dfrac{5(\sqrt{10}+\sqrt{5})}{10-5}=\sqrt{10}+\sqrt{5}=3.162+2.236=5.398$$

Mathematics
RS Agarwal
Standard IX

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