The value of 12−68+482=

12−68+482=12−68+224×24×2=12−68+232×36=12−(36+32)=12−(6+28)=6−24×2=4−2=2−2

The value of 12−68+482=

12−68+482=12−68+224×24×2=12−68+232×36=12−(36+32)=12−(6+28)=6−24×2=4−2=2−2

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The value of $\sqrt{12 - \sqrt{68 + 48 \sqrt{2}}} =$

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$1 + \sqrt{2}$

$2 + \sqrt{2}$

$1 - \sqrt{2}$

$2 - \sqrt{2}$

answer is D.

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Detailed Solution

$\sqrt{12 - \sqrt{68 + 48 \sqrt{2}}}$

$= \sqrt{12 - \sqrt{68 + 2 \sqrt{24 \times 24 \times 2}}}$

$= \sqrt{12 - \sqrt{68 + 2 \sqrt{32 \times 36}}}$

$= \sqrt{12 - (\sqrt{36} + \sqrt{32})}$

$= \sqrt{12 - (6 + 2 \sqrt{8})}$

$= \sqrt{6 - 2 \sqrt{4 \times 2}}$

$= \sqrt{4} - \sqrt{2}$

$= 2 - \sqrt{2}$

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The value of $\sqrt{12 - \sqrt{68 + 48 \sqrt{2}}} =$