Solve frac{sqrt{7}}{sqrt{11}}*sqrt{11}

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

Evaluate

$$\sqrt{7}\approx 2.645751311$$

Solution Steps

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

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

The square of \sqrt{11} is 11.

$$\frac{\sqrt{7}\sqrt{11}}{11}\sqrt{11}$$

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

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

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

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

Factor 77=11\times 7. Rewrite the square root of the product \sqrt{11\times 7} as the product of square roots \sqrt{11}\sqrt{7}.

$$\frac{\sqrt{11}\sqrt{7}\sqrt{11}}{11}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$\frac{11\sqrt{7}}{11}$$

Cancel out 11 and 11.

$$\sqrt{7}$$