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Basic of Logarithms
medium
$\sqrt {(3 + \sqrt 5 )} - \sqrt {(2 + \sqrt 3 )} = $
A
$\sqrt {(5/2)} + \sqrt {(3/2)} $
B
$\sqrt {(5/2)} - \sqrt {(3/2)} $
C
$\sqrt {(5/2)} - \sqrt {(1/2)} $
D
$\sqrt {(3/2)} - \sqrt {(1/2)} $
Solution
(b) $\sqrt {(3 + \sqrt 5 )} – \sqrt {2 + \sqrt 3 } = \sqrt {{{6 + 2\sqrt 5 } \over 2}} – \sqrt {{{4 + 2\sqrt 3 } \over 2}} $
$ = {1 \over {\sqrt 2 }}\,[(1 + \sqrt 5 ) – (1 + \sqrt 3 )] = {1 \over {\sqrt 2 }}(\sqrt 5 – \sqrt 3 ) = \sqrt {{5 \over 2}} – \sqrt {{3 \over 2}} $.
Standard 11
Mathematics
