Solve sqrt{5/11}*frac{11sqrt{7}}{7}

$$\sqrt { \frac { 5 } { 11 } } \times \frac { 11 \sqrt { 7 } } { 7 }$$

Evaluate

$$\frac{\sqrt{385}}{7}\approx 2.803059553$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{11}} as the division of square roots \frac{\sqrt{5}}{\sqrt{11}}.

$$\frac{\sqrt{5}}{\sqrt{11}}\times \frac{11\sqrt{7}}{7}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{5}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}\times \frac{11\sqrt{7}}{7}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{5}\sqrt{11}}{11}\times \frac{11\sqrt{7}}{7}$$

To multiply \sqrt{5} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{55}}{11}\times \frac{11\sqrt{7}}{7}$$

Multiply \frac{\sqrt{55}}{11} times \frac{11\sqrt{7}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{55}\times 11\sqrt{7}}{11\times 7}$$

Cancel out 11 in both numerator and denominator.

$$\frac{\sqrt{7}\sqrt{55}}{7}$$

To multiply \sqrt{7} and \sqrt{55}, multiply the numbers under the square root.

$$\frac{\sqrt{385}}{7}$$