Question

Find
the value √14 whole divided by whole root over of 6+√35+whole root over of 6-√35.
Options-
i.1
ii.2
iii.1/2
iv.3/2​

Answer 1

Your answer is " 1 "

$\frac{ \sqrt{14} }{ \sqrt{6 + \sqrt{35} } + \sqrt{6 - \sqrt{35} } } = 1$

On Rationalizing the denominator:

$⇒\frac{ \sqrt{2} \: ( \sqrt{6 - \sqrt{35} } - \sqrt{6 + \sqrt{35} } \: ) }{ - 2 \sqrt{5} }$

On Opening the brackets:

$⇒ \frac{ \sqrt{12 - 2\sqrt{35} } - \sqrt{12} + 2 \sqrt{35} }{ - 2 \sqrt{5} }$

$⇒\frac{ \sqrt{( \sqrt{5} - \sqrt{7} ) ^{2} } - \sqrt{( \sqrt{5} + \sqrt{7}) ^{2} } }{ - 2 \sqrt{5} }$

$⇒\frac{ \sqrt{7} - \sqrt{5} - \sqrt{5} - \sqrt{7} }{ - 2 \sqrt{5} }$

$⇒\frac{ - 2 \sqrt{5} }{ - 2 \sqrt{5} } = 1$