Solve sqrt{4+2/5}=

$$\sqrt{ 4+ \frac{ 2 }{ 5 } } =$$

Evaluate

$$\frac{\sqrt{110}}{5}\approx 2.097617696$$

Solution Steps

Convert 4 to fraction \frac{20}{5}.

$$\sqrt{\frac{20}{5}+\frac{2}{5}}$$

Since \frac{20}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{20+2}{5}}$$

Add 20 and 2 to get 22.

$$\sqrt{\frac{22}{5}}$$

Rewrite the square root of the division \sqrt{\frac{22}{5}} as the division of square roots \frac{\sqrt{22}}{\sqrt{5}}.

$$\frac{\sqrt{22}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{22}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{22}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{22}\sqrt{5}}{5}$$

To multiply \sqrt{22} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{110}}{5}$$