${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }} = . . . $
Medium
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c
(c) Given fraction
(c) Given fraction
\( = {{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\)
\( = {{15} \over {\sqrt {10} + 2\sqrt 5 + 2\sqrt {10} - \sqrt 5 - 4\sqrt 5 }}\)
\( = {{15} \over {3\sqrt {10} - 3\sqrt 5 }} = {5 \over {\sqrt {10} - \sqrt 5 }}\,.\,{{\sqrt {10} + \sqrt 5 } \over {\sqrt {10} + \sqrt 5 }}\)
\( = \sqrt {10} + \sqrt 5 = \sqrt 5 (\sqrt 2 + 1)\)
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