Solve 5/2sqrt{10/3}

$$\frac{ 5 }{ 2 } \sqrt{ \frac{ 10 }{ 3 } }$$

Evaluate

$$\frac{5\sqrt{30}}{6}\approx 4.564354646$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{10}{3}} as the division of square roots \frac{\sqrt{10}}{\sqrt{3}}.

$$\frac{5}{2}\times \frac{\sqrt{10}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{10}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{5}{2}\times \frac{\sqrt{10}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{5}{2}\times \frac{\sqrt{10}\sqrt{3}}{3}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{5}{2}\times \frac{\sqrt{30}}{3}$$

Multiply \frac{5}{2} times \frac{\sqrt{30}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\sqrt{30}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{5\sqrt{30}}{6}$$