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basic of algoritham — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSbasic of algoritham1 Mark
MCQ
${{\sqrt {(5/2)} + \sqrt {(7 - 3\sqrt 5 )} } \over {\sqrt {(7/2)} + \sqrt {(16 - 5\sqrt 7 )} }}=$
  • ✓
    Rational
  • B
    Surd
  • C
    Multiple of $\sqrt 7 $
  • D
    None of these
✓

Answer

Correct option: A.
Rational
a
(a) ${{\sqrt {5/2} + \sqrt {7 - 3\sqrt 5 } } \over {\sqrt {7/2} + \sqrt {16 - 5\sqrt 7 } }} = {{\sqrt 5 + \sqrt {14 - 6\sqrt 5 } } \over {\sqrt 7 + \sqrt {32 - 10\sqrt 7 } }}$

$= {{\sqrt 5 + (3 - \sqrt {5)} } \over {\sqrt 7 + (5 - \sqrt 7 )}} = {3 \over 5}$, which is rational.

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