Solve sqrt{4+12/5}

$$\sqrt{ 4+ \frac{ 12 }{ 5 } }$$

Evaluate

$$\frac{4\sqrt{10}}{5}\approx 2.529822128$$

Solution Steps

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

$$\sqrt{\frac{20}{5}+\frac{12}{5}}$$

Since \frac{20}{5} and \frac{12}{5} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{20+12}{5}}$$

Add 20 and 12 to get 32.

$$\sqrt{\frac{32}{5}}$$

Rewrite the square root of the division \sqrt{\frac{32}{5}} as the division of square roots \frac{\sqrt{32}}{\sqrt{5}}.

$$\frac{\sqrt{32}}{\sqrt{5}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Rationalize the denominator of \frac{4\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{4\sqrt{10}}{5}$$