Question : What is the value of $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}}$?
Option 1: $2\sqrt{6}$
Option 2: $4\sqrt{6}$
Option 3: $2$
Option 4: $4$
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Correct Answer: $2$
Solution : Given: $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}}$ By factorising and simplifying this expression, $\frac{\sqrt{2\times2\times2\times 3} + \sqrt{2\times2\times2\times3\times3\times3}}{\sqrt{2\times2\times2\times2\times2\times3}}$ = $\frac{\sqrt{4\times6} + \sqrt{6\times36}}{\sqrt{6\times16}}$ = $\frac{2\sqrt{6} + 6\sqrt{6}}{4\sqrt{6}}$ = $\frac{(2+6)\sqrt{6}}{4\sqrt{6}}$ = $\frac{8\sqrt{6}}{4\sqrt{6}}$ = $\frac{8}{4}$ = $2$ Hence, the correct answer is $2$.
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