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Basic of Logarithms
medium
The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $
A
$2 + \sqrt 2 $
B
$2 - \sqrt 2 $
C
$\sqrt 2 - 1$
D
None of these
Solution
(b) $\sqrt {12 – \sqrt {68 + 48\sqrt 2 } } = \sqrt {12 – \sqrt {{6^2} + {{(4\sqrt 2 )}^2} + 2.6.4\sqrt 2 } } $
$= \sqrt {12 – \sqrt {{{(6 + 4\sqrt 2 )}^2}} } $= $\sqrt {12 – 6 – 4\sqrt 2 } = \sqrt {6 – 4\sqrt 2 } $
$= \sqrt {{2^2} + {{(\sqrt 2 )}^2} – 2\,.\,2\sqrt 2 } = 2 – \sqrt 2 $.
Standard 11
Mathematics
