Solve sqrt{8/5}+6

$$\sqrt { \frac { 8 } { 5 } } + 6$$

Evaluate

$$\frac{2\sqrt{10}}{5}+6\approx 7.264911064$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\sqrt{8}}{\sqrt{5}}+6$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{5}}+6$$

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

$$\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+6$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{2}\sqrt{5}}{5}+6$$

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

$$\frac{2\sqrt{10}}{5}+6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{5}{5}.

$$\frac{2\sqrt{10}}{5}+\frac{6\times 5}{5}$$

Since \frac{2\sqrt{10}}{5} and \frac{6\times 5}{5} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{10}+6\times 5}{5}$$

Do the multiplications in 2\sqrt{10}+6\times 5.

$$\frac{2\sqrt{10}+30}{5}$$