Solve -sqrt{41/5}div1/1sqrt{7/10}

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

Evaluate

$$-\frac{7\sqrt{6}}{10}\approx -1.71464282$$

Solution Steps

Divide 1 by 1 to get 1.

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

Multiply 4 and 5 to get 20.

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

Add 20 and 1 to get 21.

$$\frac{-\sqrt{\frac{21}{5}}}{1}\sqrt{\frac{7}{10}}$$

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

$$\frac{-\frac{\sqrt{21}}{\sqrt{5}}}{1}\sqrt{\frac{7}{10}}$$

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

$$\frac{-\frac{\sqrt{21}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{1}\sqrt{\frac{7}{10}}$$

The square of \sqrt{5} is 5.

$$\frac{-\frac{\sqrt{21}\sqrt{5}}{5}}{1}\sqrt{\frac{7}{10}}$$

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

$$\frac{-\frac{\sqrt{105}}{5}}{1}\sqrt{\frac{7}{10}}$$

Anything divided by one gives itself.

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

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

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

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

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

The square of \sqrt{10} is 10.

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

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

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

Multiply -\frac{\sqrt{105}}{5} times \frac{\sqrt{70}}{10} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{-\sqrt{7350}}{5\times 10}$$

Multiply 5 and 10 to get 50.

$$\frac{-\sqrt{7350}}{50}$$

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}.

$$\frac{-35\sqrt{6}}{50}$$

Divide -35\sqrt{6} by 50 to get -\frac{7}{10}\sqrt{6}.

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