Solve frac{4sqrt{3}}{3sqrt{2}}

$$\frac { 4 \sqrt { 3 } } { 3 \sqrt { 2 } }$$

Evaluate

$$\frac{2\sqrt{6}}{3}\approx 1.632993162$$

Solution Steps

Rationalize the denominator of \frac{4\sqrt{3}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{4\sqrt{3}\sqrt{2}}{3\times 2}$$

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

$$\frac{4\sqrt{6}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{4\sqrt{6}}{6}$$

Divide 4\sqrt{6} by 6 to get \frac{2}{3}\sqrt{6}.

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