A) \[5+2\sqrt{6}\]
B) \[\frac{3+2\sqrt{6}}{2}\]
C) \[5-2\sqrt{3}\]
D) \[5+2\sqrt{3}\]
Correct Answer: A
Solution :
Given expression \[=\frac{3\sqrt{2}+2\sqrt{2}}{3\sqrt{2}-2\sqrt{3}}\] Rationalising the denominator, \[=\frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}\times \frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}\frac{{{(3\sqrt{2}+2\sqrt{3})}^{2}}}{{{(3\sqrt{2})}^{2}}-{{(2\sqrt{3})}^{2}}}\] \[=\frac{18+12+2\times 3\sqrt{2}\times 2\sqrt{3}}{18-12}\] \[=\frac{30+12\sqrt{6}}{6}=\frac{6\,\,(5+2\sqrt{6})}{6}=5+2\sqrt{6}\]
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