Solve sqrt{244/13}

$$\sqrt { \frac { 244 } { 13 } }$$

Evaluate

$$\frac{2\sqrt{793}}{13}\approx 4.332347028$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{244}{13}} as the division of square roots \frac{\sqrt{244}}{\sqrt{13}}.

$$\frac{\sqrt{244}}{\sqrt{13}}$$

Factor 244=2^{2}\times 61. Rewrite the square root of the product \sqrt{2^{2}\times 61} as the product of square roots \sqrt{2^{2}}\sqrt{61}. Take the square root of 2^{2}.

$$\frac{2\sqrt{61}}{\sqrt{13}}$$

Rationalize the denominator of \frac{2\sqrt{61}}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{2\sqrt{61}\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{2\sqrt{61}\sqrt{13}}{13}$$

To multiply \sqrt{61} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{2\sqrt{793}}{13}$$