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Question

Question: \(\frac{\sqrt{(5/2)} + \sqrt{(7 - 3\sqrt{5})}}{\sqrt{(7/2)} + \sqrt{(16 - 5\sqrt{7})}}\)=...

(5/2)+(7−35)(7/2)+(16−57)\frac{\sqrt{(5/2)} + \sqrt{(7 - 3\sqrt{5})}}{\sqrt{(7/2)} + \sqrt{(16 - 5\sqrt{7})}}=

A

Rational

B

Surd

C

Multiple of 7\sqrt{7}

D

None of these

Answer

Rational

Explanation

Solution

5/2+7−357/2+16−57=5+14−657+32−107\frac{\sqrt{5/2} + \sqrt{7 - 3\sqrt{5}}}{\sqrt{7/2} + \sqrt{16 - 5\sqrt{7}}} = \frac{\sqrt{5} + \sqrt{14 - 6\sqrt{5}}}{\sqrt{7} + \sqrt{32 - 10\sqrt{7}}}

= 5+(3−5)7+(5−7)=35\frac{\sqrt{5} + (3 - \sqrt{5)}}{\sqrt{7} + (5 - \sqrt{7})} = \frac{3}{5}, which is rational.