The value of [12 5 + 2(55) ] is - Vidyadip

MCQ

The value of $\sqrt {[12\sqrt 5 + 2\sqrt {(55)} ]} $ is

A
${5^{1/2}}[\sqrt {(11)} + 1]$
B
${5^{1/2}}[\sqrt {(11)} - 1]$
✓
${5^{1/4}}[\sqrt {(11)} + 1]$
D
${5^{1/4}}[\sqrt {(11)} - 1]$

✓

Answer

Correct option: C.

${5^{1/4}}[\sqrt {(11)} + 1]$

c
(c) $\sqrt {12\sqrt 5 + 2\sqrt {55} } = \sqrt {\sqrt 5 (12 + 2\sqrt {11} )} $

$ = {5^{1/4}}\sqrt {11 + 1 + 2\sqrt {11} } = {5^{1/4}}(\sqrt {11} + 1)$

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