Solve sqrt{88/13}

$$\sqrt { \frac { 88 } { 13 } }$$

Evaluate

$$\frac{2\sqrt{286}}{13}\approx 2.601774542$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{88}{13}} as the division of square roots \frac{\sqrt{88}}{\sqrt{13}}.

$$\frac{\sqrt{88}}{\sqrt{13}}$$

Factor 88=2^{2}\times 22. Rewrite the square root of the product \sqrt{2^{2}\times 22} as the product of square roots \sqrt{2^{2}}\sqrt{22}. Take the square root of 2^{2}.

$$\frac{2\sqrt{22}}{\sqrt{13}}$$

Rationalize the denominator of \frac{2\sqrt{22}}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{2\sqrt{22}\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{2\sqrt{22}\sqrt{13}}{13}$$

To multiply \sqrt{22} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{2\sqrt{286}}{13}$$