Solve sqrt{13/28}

$$\sqrt { \frac { 13 } { 28 } }$$

Evaluate

$$\frac{\sqrt{91}}{14}\approx 0.681385144$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{13}{28}} as the division of square roots \frac{\sqrt{13}}{\sqrt{28}}.

$$\frac{\sqrt{13}}{\sqrt{28}}$$

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}.

$$\frac{\sqrt{13}}{2\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{13}}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{13}\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{13}\sqrt{7}}{2\times 7}$$

To multiply \sqrt{13} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{91}}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$\frac{\sqrt{91}}{14}$$