Solve sqrt{11/28}=

$$\sqrt { \frac { 11 } { 28 } } =$$

Evaluate

$$\frac{\sqrt{77}}{14}\approx 0.626783171$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{11}{28}} as the division of square roots \frac{\sqrt{11}}{\sqrt{28}}.

$$\frac{\sqrt{11}}{\sqrt{28}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{7} is 7.

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

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

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

Multiply 2 and 7 to get 14.

$$\frac{\sqrt{77}}{14}$$