Solve -3/8sqrt{10}div1/2sqrt{2/5}

$$- \frac{ 3 }{ 8 } \sqrt{ 10 } \div \frac{ 1 }{ 2 } \sqrt{ \frac{ 2 }{ 5 } }$$

Evaluate

$$-\frac{3}{2}=-1.5$$

Solution Steps

Divide -\frac{3}{8}\sqrt{10} by \frac{1}{2} by multiplying -\frac{3}{8}\sqrt{10} by the reciprocal of \frac{1}{2}.

$$-\frac{3}{8}\sqrt{10}\times 2\sqrt{\frac{2}{5}}$$

Express -\frac{3}{8}\times 2 as a single fraction.

$$\frac{-3\times 2}{8}\sqrt{10}\sqrt{\frac{2}{5}}$$

Multiply -3 and 2 to get -6.

$$\frac{-6}{8}\sqrt{10}\sqrt{\frac{2}{5}}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

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

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

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

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

$$-\frac{3}{4}\sqrt{10}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

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

Multiply -\frac{3}{4} times \frac{\sqrt{10}}{5} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 4 and 5 to get 20.

$$\frac{-3\sqrt{10}}{20}\sqrt{10}$$

Express \frac{-3\sqrt{10}}{20}\sqrt{10} as a single fraction.

$$\frac{-3\sqrt{10}\sqrt{10}}{20}$$

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

$$\frac{-3\times 10}{20}$$

Multiply -3 and 10 to get -30.

$$\frac{-30}{20}$$

Reduce the fraction \frac{-30}{20} to lowest terms by extracting and canceling out 10.

$$-\frac{3}{2}$$

Factor

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$