The value of [12 - (68 + 48 2 ) ] = - Vidyadip

MCQ

The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $

A
$2 + \sqrt 2 $
✓
$2 - \sqrt 2 $
C
$\sqrt 2 - 1$
D
None of these

✓

Answer

Correct option: B.

$2 - \sqrt 2 $

b
(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 $.

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