Solve 2+sqrt{25/2}

$$2+ \sqrt{ \frac{ 25 }{ 2 } }$$

Evaluate

$$\frac{5\sqrt{2}}{2}+2\approx 5.535533906$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{2}} as the division of square roots \frac{\sqrt{25}}{\sqrt{2}}.

$$2+\frac{\sqrt{25}}{\sqrt{2}}$$

Calculate the square root of 25 and get 5.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

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