Q. $\sqrt{2 + \sqrt{5} - \sqrt{6 - 3\sqrt{5} + \sqrt{14 - 6\sqrt{5}}}}$ is equal to
A) 1
B) 2
C) 3
D) 4
Explanation
(b)
$\sqrt{2 + \sqrt{5} - \sqrt{6 - 3\sqrt{5} + \sqrt{14 - 6\sqrt{5}}}}$
$= \sqrt{2 + \sqrt{5} - \sqrt{6 - 3\sqrt{5} + \sqrt{\left( 9 + 5 - 6\sqrt{5} \right)}}}$
$= \sqrt{2 + \sqrt{5} - \sqrt{6 - 3\sqrt{5} + \sqrt{{\left( 3 - \sqrt{5} \right)\ }^{2}}}}$
$= \sqrt{2 + \sqrt{5} - \sqrt{9 - 4\sqrt{5}}}$
$= \sqrt{2 + \sqrt{5} - \sqrt{\left( - 2 + \sqrt{5} \right)^{2}}}$
$= \sqrt{2 + \sqrt{5} + 2 - \sqrt{5}} = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.