Aptitude Question ID: 107140
The value of $latex \sqrt{8-2\sqrt{15}}$ is :
[A]$latex 3-\sqrt{5}$
[B]$latex 5-\sqrt{3}$
[C]$latex \sqrt{5}-\sqrt{3}$
[D]$latex \sqrt{5}+\sqrt{3}$
$latex \mathbf{\sqrt{5}-\sqrt{3}}$
Expression = $latex \sqrt{8-2\sqrt{15}}$
$latex = \sqrt{5+3-2\sqrt{5}\times \sqrt{3}}$
$latex = \sqrt{(5)^{2}+(3)^{2}-2\sqrt{5}\times \sqrt{3}}$
$latex = \sqrt{(\sqrt{5}-\sqrt{3})^{2}} = \sqrt{5}-\sqrt{3}$
Hence option [C] is correct answer.