Solve -sqrt{41/5}divsqrt{7/10}

$$- \sqrt { 4 \frac { 1 } { 5 } } \div \sqrt { \frac { 7 } { 10 } }$$

Evaluate

$$-\sqrt{6}\approx -2.449489743$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{-\sqrt{\frac{20+1}{5}}}{\sqrt{\frac{7}{10}}}$$

Add 20 and 1 to get 21.

$$\frac{-\sqrt{\frac{21}{5}}}{\sqrt{\frac{7}{10}}}$$

Rewrite the square root of the division \sqrt{\frac{21}{5}} as the division of square roots \frac{\sqrt{21}}{\sqrt{5}}.

$$\frac{-\frac{\sqrt{21}}{\sqrt{5}}}{\sqrt{\frac{7}{10}}}$$

Rationalize the denominator of \frac{\sqrt{21}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-\frac{\sqrt{21}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{7}{10}}}$$

The square of \sqrt{5} is 5.

$$\frac{-\frac{\sqrt{21}\sqrt{5}}{5}}{\sqrt{\frac{7}{10}}}$$

To multiply \sqrt{21} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{-\frac{\sqrt{105}}{5}}{\sqrt{\frac{7}{10}}}$$

Rewrite the square root of the division \sqrt{\frac{7}{10}} as the division of square roots \frac{\sqrt{7}}{\sqrt{10}}.

$$\frac{-\frac{\sqrt{105}}{5}}{\frac{\sqrt{7}}{\sqrt{10}}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{-\frac{\sqrt{105}}{5}}{\frac{\sqrt{7}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}}$$

The square of \sqrt{10} is 10.

$$\frac{-\frac{\sqrt{105}}{5}}{\frac{\sqrt{7}\sqrt{10}}{10}}$$

To multiply \sqrt{7} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{-\frac{\sqrt{105}}{5}}{\frac{\sqrt{70}}{10}}$$

Divide -\frac{\sqrt{105}}{5} by \frac{\sqrt{70}}{10} by multiplying -\frac{\sqrt{105}}{5} by the reciprocal of \frac{\sqrt{70}}{10}.

$$\frac{\left(-\frac{\sqrt{105}}{5}\right)\times 10}{\sqrt{70}}$$

Cancel out 5, the greatest common factor in 10 and 5.

$$\frac{-2\sqrt{105}}{\sqrt{70}}$$

Rationalize the denominator of \frac{-2\sqrt{105}}{\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\frac{-2\sqrt{105}\sqrt{70}}{\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\frac{-2\sqrt{105}\sqrt{70}}{70}$$

To multiply \sqrt{105} and \sqrt{70}, multiply the numbers under the square root.

$$\frac{-2\sqrt{7350}}{70}$$

Factor 7350=35^{2}\times 6. Rewrite the square root of the product \sqrt{35^{2}\times 6} as the product of square roots \sqrt{35^{2}}\sqrt{6}. Take the square root of 35^{2}.

$$\frac{-2\times 35\sqrt{6}}{70}$$

Multiply -2 and 35 to get -70.

$$\frac{-70\sqrt{6}}{70}$$

Cancel out 70 and 70.

$$-\sqrt{6}$$