Question : $[2\sqrt{{54}}-6\sqrt{{\frac{2}{3}}}-\sqrt{96}]$ is equal to:
Option 1: $0$
Option 2: $1$
Option 3: $2$
Option 4: $\sqrt{6}$
Correct Answer: $0$
Solution :
Given: $2\sqrt{54} - 6\sqrt{\frac{2}{3}} - \sqrt{96}$
By simplifying this expression, we get:
= $2\sqrt{2\times3\times3\times 3} - (2\times3)\sqrt{\frac{2}{3}} - \sqrt{2\times 2\times 2\times 2\times 2\times 3}$
= $6\sqrt{6} - 2\sqrt{\frac{2}{3}\times9} - 4\sqrt{6}$
= $6\sqrt{6} - 2\sqrt{6} - 4\sqrt{6}$
= $6\sqrt{6} - 6\sqrt{6}$
= $0$
Hence, the correct answer is $0$.
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