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

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

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

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply 3 and 2 to get 6.

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

Divide 6\sqrt{3} by 3 to get 2\sqrt{3}.

$$2\sqrt{3}$$