Solve 5/3sqrt{5/3}

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

Evaluate

$$\frac{5\sqrt{15}}{9}\approx 2.151657415$$

Solution Steps

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply \frac{5}{3} times \frac{\sqrt{15}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 3 and 3 to get 9.

$$\frac{5\sqrt{15}}{9}$$