Solve {l}{-3/sqrt{2}}{+3}

$$\left. \begin{array} { l } { \frac { - 3 } { \sqrt { 2 } } } \\ { + 3 } \end{array} \right.$$

Evaluate

$$-\frac{3\sqrt{2}}{2}+3\approx 0.878679656$$

Short Solution Steps

Rationalize the denominator of \frac{-3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+3$$

The square of \sqrt{2} is 2.

$$\frac{-3\sqrt{2}}{2}+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{-3\sqrt{2}}{2}+\frac{3\times 2}{2}$$

Since \frac{-3\sqrt{2}}{2} and \frac{3\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-3\sqrt{2}+3\times 2}{2}$$

Do the multiplications in -3\sqrt{2}+3\times 2.

$$\frac{-3\sqrt{2}+6}{2}$$

Factor

$$\frac{3 \sqrt{2} {(\sqrt{2} - 1)}}{2} = 0.8786796564403576$$