Solve 5-1/sqrt{2}

$$5 - \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$-\frac{\sqrt{2}}{2}+5\approx 4.292893219$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

$$\frac{10-\sqrt{2}}{2}$$