Solve sqrt{5/3}sqrt{8/4}

$$\sqrt { \frac { 5 } { 3 } } \sqrt { \frac { 8 } { 4 } }$$

Evaluate

$$\frac{\sqrt{30}}{3}\approx 1.825741858$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$\frac{\sqrt{5}}{\sqrt{3}}\sqrt{\frac{8}{4}}$$

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

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{\frac{8}{4}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{5}\sqrt{3}}{3}\sqrt{\frac{8}{4}}$$

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

$$\frac{\sqrt{15}}{3}\sqrt{\frac{8}{4}}$$

Divide 8 by 4 to get 2.

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

Express \frac{\sqrt{15}}{3}\sqrt{2} as a single fraction.

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

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{3}$$