Solve sqrt{5/2}+8/2=

$$\sqrt{ \frac{ 5 }{ 2 } } + \frac{ 8 }{ 2 } =$$

Evaluate

$$\frac{\sqrt{10}}{2}+4\approx 5.58113883$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{\sqrt{5}}{\sqrt{2}}+\frac{8}{2}$$

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

$$\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{8}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{5}\sqrt{2}}{2}+\frac{8}{2}$$

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

$$\frac{\sqrt{10}}{2}+\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$\frac{\sqrt{10}}{2}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\frac{\sqrt{10}}{2}+\frac{4\times 2}{2}$$

Since \frac{\sqrt{10}}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{10}+4\times 2}{2}$$

Do the multiplications in \sqrt{10}+4\times 2.

$$\frac{\sqrt{10}+8}{2}$$