Solve [2sqrt{54}-6sqrt{2/3}-sqrt{96}]

$$[ 2 \sqrt { 54 } - 6 \sqrt { \frac { 2 } { 3 } } - \sqrt { 96 } ]$$

Evaluate

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Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$2\times 3\sqrt{6}-6\sqrt{\frac{2}{3}}-\sqrt{96}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{6}-6\sqrt{\frac{2}{3}}-\sqrt{96}$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$6\sqrt{6}-6\times \frac{\sqrt{2}}{\sqrt{3}}-\sqrt{96}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$6\sqrt{6}-6\times \frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{96}$$

The square of \sqrt{3} is 3.

$$6\sqrt{6}-6\times \frac{\sqrt{2}\sqrt{3}}{3}-\sqrt{96}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$6\sqrt{6}-6\times \frac{\sqrt{6}}{3}-\sqrt{96}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$6\sqrt{6}-2\sqrt{6}-\sqrt{96}$$

Combine 6\sqrt{6} and -2\sqrt{6} to get 4\sqrt{6}.

$$4\sqrt{6}-\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$4\sqrt{6}-4\sqrt{6}$$

Combine 4\sqrt{6} and -4\sqrt{6} to get 0.

$$0$$

Factor

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