Solve frac{sqrt{10}}{6}*frac{4sqrt{3}}{sqrt{2}}

$$\frac { \sqrt { 10 } } { 6 } \cdot \frac { 4 \sqrt { 3 } } { \sqrt { 2 } }$$

Evaluate

$$\frac{2\sqrt{15}}{3}\approx 2.581988897$$

Solution Steps

Rationalize the denominator of \frac{4\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{10}}{6}\times \frac{4\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{10}}{6}\times \frac{4\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{6}\times \frac{4\sqrt{6}}{2}$$

Divide 4\sqrt{6} by 2 to get 2\sqrt{6}.

$$\frac{\sqrt{10}}{6}\times 2\sqrt{6}$$

Cancel out 6, the greatest common factor in 2 and 6.

$$\frac{\sqrt{10}}{3}\sqrt{6}$$

Express \frac{\sqrt{10}}{3}\sqrt{6} as a single fraction.

$$\frac{\sqrt{10}\sqrt{6}}{3}$$

To multiply \sqrt{10} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{60}}{3}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

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