Q. $\sqrt{12 - \sqrt{68 + 48\sqrt{2}}}$ is equal to
A) $\sqrt{2} - 3$
B) $2 + \sqrt{2}$
C) $2 - \sqrt{2}$
D) $6 - 2\sqrt{8}$
Explanation
(c)
$\sqrt{12 - \sqrt{68 + 48\sqrt{2}}}$
$= \sqrt{12 - \sqrt{(6)^{2} + \left( 4\sqrt{2} \right)^{2} + 2 \times 6 \times 4\sqrt{2}}}$
$= \sqrt{12 - 6 - 4\sqrt{2}} = \sqrt{6 - 4\sqrt{2}}$
$= \sqrt{\left( 2 - \sqrt{2} \right)^{2}} = 2 - \sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.