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: $\sqrt{6}$
Answer (1)
19th Jan, 2024
Correct Answer: $0$
Solution :
Given:
$2\sqrt{54}-6\sqrt{\frac{2}{3}}-\sqrt{96}$
= $6\sqrt{6}-6\sqrt{\frac{2}{3}}-4\sqrt{6}$
= $2\sqrt{6}-6\sqrt{\frac{2}{3}}$
= $2\sqrt{2}\sqrt{3}-6\frac{\sqrt{2}}{\sqrt{3}}$
= $\frac{2\sqrt{2}×3-6\sqrt{2}}{\sqrt{3}}$
= $\frac{6\sqrt{2}-6\sqrt{2}}{\sqrt{3}}$
= $0$
Hence, the correct answer is $0$.
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