Aptitude Question ID: 107146
The simplified form of
$latex \frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}&s=1$ is :
[A]$latex \sqrt{3}$
[B]$latex 3-\sqrt{3}$
[C]$latex 3\sqrt{3}$
[D]$latex 5-\sqrt{3}$
$latex \mathbf{3-\sqrt{3}}$
$latex \frac{1}{\sqrt{3}+\sqrt{4}}&s=1$
$latex = \frac{1}{\sqrt{3}+\sqrt{4}}\times \frac{\sqrt{4}-\sqrt{3}}{\sqrt{4}-\sqrt{3}}&s=1$
$latex = \frac{\sqrt{4}-\sqrt{3}}{4-3} = \sqrt{4}-\sqrt{3}&s=1$
$latex similarly,\ \frac{1}{\sqrt{4}+\sqrt{5}} = \sqrt{5}-\sqrt{4}\ ……\ so\ on.&s=1$
∴ Expression =
$latex = \sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+\sqrt{6}-\sqrt{5}+\sqrt{7}-\sqrt{6}+\sqrt{8}-\sqrt{7}+\sqrt{9}-\sqrt{8} = \sqrt{9}-\sqrt{3} = 3-\sqrt{3}$
Hence option [B] is correct answer.