Solve sqrt{5/3}*sqrt{6}=

$$\sqrt { \frac { 5 } { 3 } } \times \sqrt { 6 } =$$

Evaluate

$$\sqrt{10}\approx 3.16227766$$

Solution Steps

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

$$\frac{\sqrt{5}}{\sqrt{3}}\sqrt{6}$$

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

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{6}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{5}\sqrt{3}}{3}\sqrt{6}$$

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

$$\frac{\sqrt{15}}{3}\sqrt{6}$$

Express \frac{\sqrt{15}}{3}\sqrt{6} as a single fraction.

$$\frac{\sqrt{15}\sqrt{6}}{3}$$

To multiply \sqrt{15} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{90}}{3}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

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

Cancel out 3 and 3.

$$\sqrt{10}$$