Solve 4/3sqrt{12}*2/3sqrt{6}

$$\frac { 4 } { 3 } \sqrt { 12 } \times \frac { 2 } { 3 } \sqrt { 6 }$$

Evaluate

$$\frac{16\sqrt{2}}{3}\approx 7.542472333$$

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}.

$$\frac{4}{3}\sqrt{6}\sqrt{2}\times \frac{2}{3}\sqrt{6}$$

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

$$\frac{4}{3}\times 6\times \frac{2}{3}\sqrt{2}$$

Express \frac{4}{3}\times 6 as a single fraction.

$$\frac{4\times 6}{3}\times \frac{2}{3}\sqrt{2}$$

Multiply 4 and 6 to get 24.

$$\frac{24}{3}\times \frac{2}{3}\sqrt{2}$$

Divide 24 by 3 to get 8.

$$8\times \frac{2}{3}\sqrt{2}$$

Express 8\times \frac{2}{3} as a single fraction.

$$\frac{8\times 2}{3}\sqrt{2}$$

Multiply 8 and 2 to get 16.

$$\frac{16}{3}\sqrt{2}$$