Solve -2sqrt{2}*3sqrt{5}div5sqrt{21/3}

$$- 2 \sqrt { 2 } \times 3 \sqrt { 5 } \div 5 \sqrt { 2 \frac { 1 } { 3 } }$$

Evaluate

$$-\frac{2\sqrt{210}}{5}\approx -5.796550698$$

Solution Steps

Multiply 3 and -2 to get -6.

$$\frac{-6\sqrt{2}\sqrt{5}}{5}\sqrt{\frac{2\times 3+1}{3}}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{-6\sqrt{10}}{5}\sqrt{\frac{2\times 3+1}{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{-6\sqrt{10}}{5}\sqrt{\frac{6+1}{3}}$$

Add 6 and 1 to get 7.

$$\frac{-6\sqrt{10}}{5}\sqrt{\frac{7}{3}}$$

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

$$\frac{-6\sqrt{10}}{5}\times \frac{\sqrt{7}}{\sqrt{3}}$$

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

$$\frac{-6\sqrt{10}}{5}\times \frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{-6\sqrt{10}}{5}\times \frac{\sqrt{7}\sqrt{3}}{3}$$

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

$$\frac{-6\sqrt{10}}{5}\times \frac{\sqrt{21}}{3}$$

Multiply \frac{-6\sqrt{10}}{5} times \frac{\sqrt{21}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-6\sqrt{10}\sqrt{21}}{5\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-2\sqrt{10}\sqrt{21}}{5}$$

To multiply \sqrt{10} and \sqrt{21}, multiply the numbers under the square root.

$$\frac{-2\sqrt{210}}{5}$$