SSC Sample Paper Mock Test-7 SSC CGL Tear-II Paper-1

Which is the greatest among \[(\sqrt{19}-\sqrt{17}),\]\[(\sqrt{13}-\sqrt{11}),\]\[(\sqrt{7}-\sqrt{5})\]and \[(\sqrt{5}-\sqrt{3})?\]

A) 4.05 cm

B) 4 cm

C) 3.5 cm

D) 3 cm

Correct Answer: D

Solution :

\[\sqrt{19}-\sqrt{17}=\frac{(\sqrt{19}-\sqrt{17})\times (\sqrt{19}\times \sqrt{17})}{\sqrt{19}+\sqrt{17}}\]

\[\frac{19-17}{\sqrt{19}+\sqrt{17}}=\frac{2}{\sqrt{19}+\sqrt{17}}\]

Similarly, \[\sqrt{13}-\sqrt{11}=\frac{2}{\sqrt{13}+\sqrt{11}}\]

\[\sqrt{7}-\sqrt{5}=\frac{2}{\sqrt{7}+\sqrt{5}}\]

\[\sqrt{5}-\sqrt{3}=\frac{2}{\sqrt{5}+\sqrt{3}}\]

Clearly, \[\sqrt{5}-\sqrt{3}\]is the greatest.