Solve sqrt{28/31}

$$\sqrt { \frac { 28 } { 31 } }$$

Evaluate

$$\frac{2\sqrt{217}}{31}\approx 0.950381927$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{28}{31}} as the division of square roots \frac{\sqrt{28}}{\sqrt{31}}.

$$\frac{\sqrt{28}}{\sqrt{31}}$$

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}.

$$\frac{2\sqrt{7}}{\sqrt{31}}$$

Rationalize the denominator of \frac{2\sqrt{7}}{\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$\frac{2\sqrt{7}\sqrt{31}}{\left(\sqrt{31}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$\frac{2\sqrt{7}\sqrt{31}}{31}$$

To multiply \sqrt{7} and \sqrt{31}, multiply the numbers under the square root.

$$\frac{2\sqrt{217}}{31}$$