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

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

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 3 and 3 to get 9.

$$9\times \frac{2}{3}\sqrt{2}$$

Express 9\times \frac{2}{3} as a single fraction.

$$\frac{9\times 2}{3}\sqrt{2}$$

Multiply 9 and 2 to get 18.

$$\frac{18}{3}\sqrt{2}$$

Divide 18 by 3 to get 6.

$$6\sqrt{2}$$