Solve sqrt{3}*frac{sqrt{6}}{3}div1/sqrt{2}

$$\sqrt { 3 } \times \frac { \sqrt { 6 } } { 3 } \div \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$2$$

Solution Steps

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

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

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Divide \frac{\sqrt{3}\sqrt{6}}{3} by \frac{\sqrt{2}}{2} by multiplying \frac{\sqrt{3}\sqrt{6}}{3} by the reciprocal of \frac{\sqrt{2}}{2}.

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

Rationalize the denominator of \frac{\sqrt{3}\sqrt{6}\times 2}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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

Multiply 3 and 2 to get 6.

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

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

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

Multiply 6 and 2 to get 12.

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

Multiply 3 and 2 to get 6.

$$\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$2$$

Factor

$$2$$