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Basic of Logarithms
medium
${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }} = . . . $
A
$\sqrt 5 (5 + \sqrt 2 )$
B
$\sqrt 5 (2 + \sqrt 2 )$
C
$\sqrt 5 (1 + \sqrt 2 )$
D
$\sqrt 5 (3 + \sqrt 2 )$
Solution
(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)$
Standard 11
Mathematics
