Solve sqrt{7/11}*(sqrt{4/7}divsqrt{1/11})

$$\sqrt { \frac { 7 } { 11 } } \cdot ( \sqrt { \frac { 4 } { 7 } } \div \sqrt { \frac { 1 } { 11 } } )$$

Evaluate

$$2$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{11}} as the division of square roots \frac{\sqrt{7}}{\sqrt{11}}.

$$\frac{\sqrt{7}}{\sqrt{11}}\times \frac{\sqrt{\frac{4}{7}}}{\sqrt{\frac{1}{11}}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{7}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}\times \frac{\sqrt{\frac{4}{7}}}{\sqrt{\frac{1}{11}}}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{7}\sqrt{11}}{11}\times \frac{\sqrt{\frac{4}{7}}}{\sqrt{\frac{1}{11}}}$$

To multiply \sqrt{7} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{77}}{11}\times \frac{\sqrt{\frac{4}{7}}}{\sqrt{\frac{1}{11}}}$$

Rewrite the square root of the division \sqrt{\frac{4}{7}} as the division of square roots \frac{\sqrt{4}}{\sqrt{7}}.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{\sqrt{4}}{\sqrt{7}}}{\sqrt{\frac{1}{11}}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2}{\sqrt{7}}}{\sqrt{\frac{1}{11}}}$$

Rationalize the denominator of \frac{2}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2\sqrt{7}}{\left(\sqrt{7}\right)^{2}}}{\sqrt{\frac{1}{11}}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2\sqrt{7}}{7}}{\sqrt{\frac{1}{11}}}$$

Rewrite the square root of the division \sqrt{\frac{1}{11}} as the division of square roots \frac{\sqrt{1}}{\sqrt{11}}.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2\sqrt{7}}{7}}{\frac{\sqrt{1}}{\sqrt{11}}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2\sqrt{7}}{7}}{\frac{1}{\sqrt{11}}}$$

Rationalize the denominator of \frac{1}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2\sqrt{7}}{7}}{\frac{\sqrt{11}}{\left(\sqrt{11}\right)^{2}}}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{77}}{11}\times \frac{\frac{2\sqrt{7}}{7}}{\frac{\sqrt{11}}{11}}$$

Divide \frac{2\sqrt{7}}{7} by \frac{\sqrt{11}}{11} by multiplying \frac{2\sqrt{7}}{7} by the reciprocal of \frac{\sqrt{11}}{11}.

$$\frac{\sqrt{77}}{11}\times \frac{2\sqrt{7}\times 11}{7\sqrt{11}}$$

Rationalize the denominator of \frac{2\sqrt{7}\times 11}{7\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{77}}{11}\times \frac{2\sqrt{7}\times 11\sqrt{11}}{7\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{77}}{11}\times \frac{2\sqrt{7}\times 11\sqrt{11}}{7\times 11}$$

Multiply 2 and 11 to get 22.

$$\frac{\sqrt{77}}{11}\times \frac{22\sqrt{7}\sqrt{11}}{7\times 11}$$

To multiply \sqrt{7} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{77}}{11}\times \frac{22\sqrt{77}}{7\times 11}$$

Multiply 7 and 11 to get 77.

$$\frac{\sqrt{77}}{11}\times \frac{22\sqrt{77}}{77}$$

Divide 22\sqrt{77} by 77 to get \frac{2}{7}\sqrt{77}.

$$\frac{\sqrt{77}}{11}\times \frac{2}{7}\sqrt{77}$$

Multiply \frac{\sqrt{77}}{11} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{77}\times 2}{11\times 7}\sqrt{77}$$

Express \frac{\sqrt{77}\times 2}{11\times 7}\sqrt{77} as a single fraction.

$$\frac{\sqrt{77}\times 2\sqrt{77}}{11\times 7}$$

Multiply \sqrt{77} and \sqrt{77} to get 77.

$$\frac{77\times 2}{11\times 7}$$

Cancel out 7\times 11 in both numerator and denominator.

$$2$$

Factor

$$2$$