Solve frac{(2sqrt{2}+3sqrt{2})*(-1/6)}{sqrt{2}}=

$$\frac { ( 2 \sqrt { 2 } + 3 \sqrt { 2 } ) \times ( - \frac { 1 } { 6 } ) } { \sqrt { 2 } } =$$

Evaluate

$$-\frac{5}{6}\approx -0.833333333$$

Solution Steps

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$\frac{5\sqrt{2}\left(-\frac{1}{6}\right)}{\sqrt{2}}$$

Express 5\left(-\frac{1}{6}\right) as a single fraction.

$$\frac{\frac{5\left(-1\right)}{6}\sqrt{2}}{\sqrt{2}}$$

Multiply 5 and -1 to get -5.

$$\frac{\frac{-5}{6}\sqrt{2}}{\sqrt{2}}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$\frac{-\frac{5}{6}\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{-\frac{5}{6}\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-\frac{5}{6}\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-\frac{5}{6}\sqrt{2}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{-\frac{5}{6}\times 2}{2}$$

Express -\frac{5}{6}\times 2 as a single fraction.

$$\frac{\frac{-5\times 2}{6}}{2}$$

Multiply -5 and 2 to get -10.

$$\frac{\frac{-10}{6}}{2}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{5}{3}}{2}$$

Express \frac{-\frac{5}{3}}{2} as a single fraction.

$$\frac{-5}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{-5}{6}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$-\frac{5}{6}$$

Factor

$$-\frac{5}{6} = -0.8333333333333334$$