Solve sqrt{2}*1/3sqrt{3}*sqrt{6}

$$\sqrt { 2 } \cdot \frac { 1 } { 3 } \sqrt { 3 } \cdot \sqrt { 6 }$$

Evaluate

$$2$$

Solution Steps

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

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

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

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

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

Cancel out 3 and 3.

$$2$$

Factor

$$2$$