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

$$\frac{3\sqrt{3}}{4}-\frac{75}{8}\approx -8.075961894$$

Short 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.

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

Rewrite the square root of the division \sqrt{\frac{27}{16}} as the division of square roots \frac{\sqrt{27}}{\sqrt{16}}.

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

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-6+\frac{3\sqrt{3}}{\sqrt{16}}-\frac{1}{8}-\frac{13}{4}$$

Calculate the square root of 16 and get 4.

$$-6+\frac{3\sqrt{3}}{4}-\frac{1}{8}-\frac{13}{4}$$

Subtract \frac{1}{8} from -6 to get -\frac{49}{8}.

$$-\frac{49}{8}+\frac{3\sqrt{3}}{4}-\frac{13}{4}$$

Subtract \frac{13}{4} from -\frac{49}{8} to get -\frac{75}{8}.

$$-\frac{75}{8}+\frac{3\sqrt{3}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 4 is 8. Multiply \frac{3\sqrt{3}}{4} times \frac{2}{2}.

$$-\frac{75}{8}+\frac{2\times 3\sqrt{3}}{8}$$

Since -\frac{75}{8} and \frac{2\times 3\sqrt{3}}{8} have the same denominator, add them by adding their numerators.

$$\frac{-75+2\times 3\sqrt{3}}{8}$$

Do the multiplications in -75+2\times 3\sqrt{3}.

$$\frac{-75+6\sqrt{3}}{8}$$

Factor

$$\frac{3 {(2 \sqrt{3} - 25)}}{8} = -8.075961894323342$$