A) \[\sqrt{3}+\sqrt{2}\]
B) \[\sqrt{3}-\sqrt{2}\]
C) \[\sqrt{2}\pm \sqrt{3}\]
D) \[\sqrt{2}-\sqrt{3}\]
Correct Answer: A
Solution :
\[\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\times \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\] \[=\frac{{{(\sqrt{3}+\sqrt{2})}^{2}}}{3-2}=\frac{3+2+2\sqrt{6}}{1}=5+2\sqrt{6}\] \[\therefore \] Required square root\[=\sqrt{5+2\sqrt{6}}\] \[=\sqrt{{{(\sqrt{3}+\sqrt{2})}^{2}}}=\sqrt{3}+\sqrt{2}\]
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