Solve sqrt{30}*sqrt{5/3}

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

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

Solution Steps

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

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

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

$$\sqrt{30}\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

$$\sqrt{30}\times \frac{\sqrt{15}}{3}$$

Express \sqrt{30}\times \frac{\sqrt{15}}{3} as a single fraction.

$$\frac{\sqrt{30}\sqrt{15}}{3}$$

Factor 30=15\times 2. Rewrite the square root of the product \sqrt{15\times 2} as the product of square roots \sqrt{15}\sqrt{2}.

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

Multiply \sqrt{15} and \sqrt{15} to get 15.

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

Divide 15\sqrt{2} by 3 to get 5\sqrt{2}.

$$5\sqrt{2}$$