Question : $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}}$ is equal to:
Option 1: $3\sqrt{6}$
Option 2: $2\sqrt{6}$
Option 3: $4\sqrt{6}$
Option 4: $2$
Correct Answer: $2$
Solution : Given $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}}$ Simplifying this expression by factorising the values, $\frac{\sqrt{2\times2\times2\times 3} + \sqrt{2\times2\times2\times3\times3\times3}}{\sqrt{2\times2\times2\times2\times2\times3}}$ = $\frac{\sqrt{4\times6} + \sqrt{6\times36}}{\sqrt{6\times16}}$ = $\frac{2\sqrt{6} + 6\sqrt{6}}{4\sqrt{6}}$ = $\frac{8\sqrt{6}}{4\sqrt{6}}$ = $\frac{8}{4}$ = $2$ Hence, the correct answer is 2.
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