Solve 4(sqrt{23}-2-11/4-3/4):(5/6)

$$4 ( \sqrt { 23 } - 2 - \frac { 11 } { 4 } - \frac { 3 } { 4 } ) : ( \frac { 5 } { 6 } )$$

Evaluate

$$\frac{24\sqrt{23}-132}{5}\approx -3.380008688$$

Solution Steps

Convert -2 to fraction -\frac{8}{4}.

$$\frac{4\left(\sqrt{23}-\frac{8}{4}-\frac{11}{4}-\frac{3}{4}\right)}{\frac{5}{6}}$$

Since -\frac{8}{4} and \frac{11}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(\sqrt{23}+\frac{-8-11}{4}-\frac{3}{4}\right)}{\frac{5}{6}}$$

Subtract 11 from -8 to get -19.

$$\frac{4\left(\sqrt{23}-\frac{19}{4}-\frac{3}{4}\right)}{\frac{5}{6}}$$

Since -\frac{19}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(\sqrt{23}+\frac{-19-3}{4}\right)}{\frac{5}{6}}$$

Subtract 3 from -19 to get -22.

$$\frac{4\left(\sqrt{23}+\frac{-22}{4}\right)}{\frac{5}{6}}$$

Reduce the fraction \frac{-22}{4} to lowest terms by extracting and canceling out 2.

$$\frac{4\left(\sqrt{23}-\frac{11}{2}\right)}{\frac{5}{6}}$$

Divide 4\left(\sqrt{23}-\frac{11}{2}\right) by \frac{5}{6} to get \frac{24}{5}\left(\sqrt{23}-\frac{11}{2}\right).

$$\frac{24}{5}\left(\sqrt{23}-\frac{11}{2}\right)$$

Use the distributive property to multiply \frac{24}{5} by \sqrt{23}-\frac{11}{2}.

$$\frac{24}{5}\sqrt{23}+\frac{24}{5}\left(-\frac{11}{2}\right)$$

Multiply \frac{24}{5} times -\frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{24}{5}\sqrt{23}+\frac{24\left(-11\right)}{5\times 2}$$

Do the multiplications in the fraction \frac{24\left(-11\right)}{5\times 2}.

$$\frac{24}{5}\sqrt{23}+\frac{-264}{10}$$

Reduce the fraction \frac{-264}{10} to lowest terms by extracting and canceling out 2.

$$\frac{24}{5}\sqrt{23}-\frac{132}{5}$$

Factor

$$\frac{12 {(2 \sqrt{23} - 11)}}{5} = -3.380008688098948$$