Solve 4sqrt{5/11}

$$4 \sqrt { \frac { 5 } { 11 } }$$

Evaluate

$$\frac{4\sqrt{55}}{11}\approx 2.69679945$$

Solution Steps

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

$$4\times \frac{\sqrt{5}}{\sqrt{11}}$$

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

$$4\times \frac{\sqrt{5}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$4\times \frac{\sqrt{5}\sqrt{11}}{11}$$

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

$$4\times \frac{\sqrt{55}}{11}$$

Express 4\times \frac{\sqrt{55}}{11} as a single fraction.

$$\frac{4\sqrt{55}}{11}$$