Solve 5+5*55/55sqrt{2}

$$5+5 \cdot \frac{ 55 }{ 55 \sqrt{ 2 } }$$

Evaluate

$$\frac{5\sqrt{2}}{2}+5\approx 8.535533906$$

Short Solution Steps

Rationalize the denominator of \frac{55}{55\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$5+5\times \frac{55\sqrt{2}}{55\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$5+5\times \frac{55\sqrt{2}}{55\times 2}$$

Cancel out 55 in both numerator and denominator.

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

Express 5\times \frac{\sqrt{2}}{2} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

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

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

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

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

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

Factor

$$\frac{5 \sqrt{2} {(\sqrt{2} + 1)}}{2} = 8.535533905932738$$