Solve sqrt{9/5}sqrt{2/3}

$$\sqrt { \frac { 9 } { 5 } } \sqrt { \frac { 2 } { 3 } }$$

Evaluate

$$\frac{\sqrt{30}}{5}\approx 1.095445115$$

Solution Steps

To multiply \sqrt{\frac{9}{5}} and \sqrt{\frac{2}{3}}, multiply the numbers under the square root.

$$\sqrt{\frac{6}{5}}$$

Rewrite the square root of the division \sqrt{\frac{6}{5}} as the division of square roots \frac{\sqrt{6}}{\sqrt{5}}.

$$\frac{\sqrt{6}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{5}$$