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

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

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

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

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

Multiply 3 and 2 to get 6.

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

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

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

$$2\sqrt{6}$$