Solve 36/5:(-5/6)^-1+sqrt{27/16-1/8}-frac{13}{4}=

$$\frac { 36 } { 5 } : ( - \frac { 5 } { 6 } ) ^ { - 1 } + \sqrt { \frac { 27 } { 16 } - \frac { 1 } { 8 } } - \frac { 13 } { 4 } =$$

Evaluate

$$-8$$

Solution Steps

Calculate -\frac{5}{6} to the power of -1 and get -\frac{6}{5}.

$$\frac{\frac{36}{5}}{-\frac{6}{5}}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}$$

Divide \frac{36}{5} by -\frac{6}{5} by multiplying \frac{36}{5} by the reciprocal of -\frac{6}{5}.

$$\frac{36}{5}\left(-\frac{5}{6}\right)+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}$$

Multiply \frac{36}{5} and -\frac{5}{6} to get -6.

$$-6+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}$$

Subtract \frac{1}{8} from \frac{27}{16} to get \frac{25}{16}.

$$-6+\sqrt{\frac{25}{16}}-\frac{13}{4}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$-6+\frac{5}{4}-\frac{13}{4}$$

Add -6 and \frac{5}{4} to get -\frac{19}{4}.

$$-\frac{19}{4}-\frac{13}{4}$$

Subtract \frac{13}{4} from -\frac{19}{4} to get -8.

$$-8$$

Factor

$$-8$$