Solve (2/3sqrt{6})(2/6sqrt{12})

$$( \frac { 2 } { 3 } \sqrt { 6 } ) ( \frac { 2 } { 6 } \sqrt { 12 } )$$

Evaluate

$$\frac{4\sqrt{2}}{3}\approx 1.885618083$$

Solution Steps

Factor 12=6\times 2. Rewrite the square root of the product \sqrt{6\times 2} as the product of square roots \sqrt{6}\sqrt{2}.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

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

Express \frac{2}{3}\times 6 as a single fraction.

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

Multiply 2 and 6 to get 12.

$$\frac{12}{3}\times \frac{2}{6}\sqrt{2}$$

Divide 12 by 3 to get 4.

$$4\times \frac{2}{6}\sqrt{2}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$4\times \frac{1}{3}\sqrt{2}$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{4}{3}\sqrt{2}$$