The correct option is D 2√(10 √(84)) (D) 1/√(12+√(140))+1/√(8 √(60)) =1/√(12+2√(35))+1/√(8 2√(15)) =1/√(7)+√(5)+1/√(5) √(3) =√(7)+√(3) ...

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Addition of Rational Expressions

1√√12+√140+1√...

Question

$\frac{1}{\sqrt{\sqrt{12} + \sqrt{140}}} + \frac{1}{\sqrt{8 - \sqrt{60}}} =$

\frac{2}{\sqrt{10 + \sqrt{84}}}

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\frac{1}{\sqrt{10 + \sqrt{84}}}

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\frac{2}{\sqrt{10 - \sqrt{84}}}

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Solution

The correct option is D $\frac{2}{\sqrt{10 - \sqrt{84}}}$
(D) $\frac{1}{\sqrt{12 + \sqrt{140}}} + \frac{1}{\sqrt{8 - \sqrt{60}}}$
$= \frac{1}{\sqrt{12 + 2 \sqrt{35}}} + \frac{1}{\sqrt{8 - 2 \sqrt{15}}}$
$= \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} - \sqrt{3}}$
$= \frac{\sqrt{7} + \sqrt{3}}{2}$
$= \frac{2}{\sqrt{7} - \sqrt{3}}$

$= \frac{2}{\sqrt{10 - \sqrt{84}}}$

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