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

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

Evaluate

$$2$$

Solution Steps

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{3} is 3.

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

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}.

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

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

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

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

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

Multiply 2 and 3 to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$