${{\sqrt {(5/2)} + \sqrt {(7 - 3\sqrt 5 )} } \over {\sqrt {(7/2)} + \sqrt {(16 - 5\sqrt 7 )} }}=$
Medium
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a
(a) \({{\sqrt {5/2} + \sqrt {7 - 3\sqrt 5 } } \over {\sqrt {7/2} + \sqrt {16 - 5\sqrt 7 } }} = {{\sqrt 5 + \sqrt {14 - 6\sqrt 5 } } \over {\sqrt 7 + \sqrt {32 - 10\sqrt 7 } }}\)
(a) \({{\sqrt {5/2} + \sqrt {7 - 3\sqrt 5 } } \over {\sqrt {7/2} + \sqrt {16 - 5\sqrt 7 } }} = {{\sqrt 5 + \sqrt {14 - 6\sqrt 5 } } \over {\sqrt 7 + \sqrt {32 - 10\sqrt 7 } }}\)
\(= {{\sqrt 5 + (3 - \sqrt {5)} } \over {\sqrt 7 + (5 - \sqrt 7 )}} = {3 \over 5}\), which is rational.
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