Question

EVALUATE:-
$\frac{15}{ \sqrt{10} + \sqrt{20} + \sqrt{40 } - \sqrt{5} - \sqrt{80} }$
PLZ FAST​

Answer 1

$\huge\rm\color{coral} Solution$

$\sf{\frac{15}{ \sqrt{10} + \sqrt{20} + \sqrt{40 } - \sqrt{5} - \sqrt{80} }}$

$\implies \sf \frac{15}{ \sqrt{10} + \sqrt{2 \times 2 \times 5} + \sqrt{2 \times 2 \times 10} - \sqrt{5} - \sqrt{4 \times 4 \times 5} }$

$\implies\sf{\frac{15}{ \sqrt{10} + 2\sqrt{5} +2 \sqrt{10 } - \sqrt{5} - 4\sqrt{5} }}$

$\implies\sf{\frac{15}{ 3\sqrt{10} -3 \sqrt{5} }}$

$\implies\sf{\frac{15}{ 3(\sqrt{10} -\sqrt{5}) }}$

$\implies\sf{\frac{5}{ \sqrt{10} -\sqrt{5}}}$