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

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

Evaluate

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

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 5 and 2 to get 10.

$$\frac{10}{2}\left(-\frac{1}{6}\right)$$

Divide 10 by 2 to get 5.

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

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

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

Multiply 5 and -1 to get -5.

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

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

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

Factor

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