Solve frac{2sqrt{3}}{3sqrt{5}}

$$\frac { 2 \sqrt { 3 } } { 3 \sqrt { 5 } }$$

Evaluate

$$\frac{2\sqrt{15}}{15}\approx 0.516397779$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{3}}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{3}\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{3}\sqrt{5}}{3\times 5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{15}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{2\sqrt{15}}{15}$$