Solve frac{-3sqrt{10}}{4}div1/2sqrt{2/5}

$$\frac { - 3 \sqrt { 10 } } { 4 } \div \frac { 1 } { 2 } \sqrt { \frac { 2 } { 5 } }$$

Evaluate

$$-3$$

Solution Steps

Divide \frac{-3\sqrt{10}}{4} by \frac{1}{2} by multiplying \frac{-3\sqrt{10}}{4} by the reciprocal of \frac{1}{2}.

$$\frac{-3\sqrt{10}\times 2}{4}\sqrt{\frac{2}{5}}$$

Multiply -3 and 2 to get -6.

$$\frac{-6\sqrt{10}}{4}\sqrt{\frac{2}{5}}$$

Divide -6\sqrt{10} by 4 to get -\frac{3}{2}\sqrt{10}.

$$-\frac{3}{2}\sqrt{10}\sqrt{\frac{2}{5}}$$

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

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

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

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

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

Multiply -\frac{3}{2} times \frac{\sqrt{10}}{5} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 5 to get 10.

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

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

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

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{-3\times 10}{10}$$

Cancel out 10 and 10.

$$-3$$

Factor

$$-3$$