Solve 2sqrt{3}*(-sqrt{7/3})*(-5sqrt{2})

$$2 \sqrt { 3 } \times ( - \sqrt { \frac { 7 } { 3 } } ) \times ( - 5 \sqrt { 2 } )$$

Evaluate

$$10\sqrt{14}\approx 37.416573868$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

$$2\sqrt{3}\left(-\frac{\sqrt{7}}{\sqrt{3}}\right)\left(-5\right)\sqrt{2}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\sqrt{3}\left(-\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)\left(-5\right)\sqrt{2}$$

The square of \sqrt{3} is 3.

$$2\sqrt{3}\left(-\frac{\sqrt{7}\sqrt{3}}{3}\right)\left(-5\right)\sqrt{2}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$2\sqrt{3}\left(-\frac{\sqrt{21}}{3}\right)\left(-5\right)\sqrt{2}$$

Multiply 2 and -5 to get -10.

$$-10\sqrt{3}\left(-\frac{\sqrt{21}}{3}\right)\sqrt{2}$$

Multiply -10 and -1 to get 10.

$$10\sqrt{3}\times \frac{\sqrt{21}}{3}\sqrt{2}$$

Express \sqrt{3}\times \frac{\sqrt{21}}{3} as a single fraction.

$$10\times \frac{\sqrt{3}\sqrt{21}}{3}\sqrt{2}$$

Express \frac{\sqrt{3}\sqrt{21}}{3}\sqrt{2} as a single fraction.

$$10\times \frac{\sqrt{3}\sqrt{21}\sqrt{2}}{3}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$10\times \frac{\sqrt{3}\sqrt{3}\sqrt{7}\sqrt{2}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$10\times \frac{3\sqrt{7}\sqrt{2}}{3}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$10\times \frac{3\sqrt{14}}{3}$$

Cancel out 3 and 3.

$$10\sqrt{14}$$