Solve {l}{11*sqrt[3]{27}-14*15/5-59+frac{sqrt{49}}{7}+13}{2*3^2/4^2+45/2,16-72/9}

$$\left. \begin{array} { l } { 11 \cdot \sqrt[ 3 ] { 27 } - 14 \cdot \frac { 15 } { 5 } - 59 + \frac { \sqrt { 49 } } { 7 } + 13 } \\ { 2 \cdot \frac { 3 ^ { 2 } } { 4 ^ { 2 } } + \frac { 45 } { 2 } , 16 - \frac { 72 } { 9 } } \end{array} \right.$$

Sort

$$-54,8,\frac{189}{8}$$

Solution Steps

Calculate \sqrt[3]{27} and get 3.

$$sort(11\times 3-14\times \frac{15}{5}-59+\frac{\sqrt{49}}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Multiply 11 and 3 to get 33.

$$sort(33-14\times \frac{15}{5}-59+\frac{\sqrt{49}}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Divide 15 by 5 to get 3.

$$sort(33-14\times 3-59+\frac{\sqrt{49}}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Multiply 14 and 3 to get 42.

$$sort(33-42-59+\frac{\sqrt{49}}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Subtract 42 from 33 to get -9.

$$sort(-9-59+\frac{\sqrt{49}}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Subtract 59 from -9 to get -68.

$$sort(-68+\frac{\sqrt{49}}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Calculate the square root of 49 and get 7.

$$sort(-68+\frac{7}{7}+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Divide 7 by 7 to get 1.

$$sort(-68+1+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Add -68 and 1 to get -67.

$$sort(-67+13,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Add -67 and 13 to get -54.

$$sort(-54,2\times \frac{3^{2}}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Calculate 3 to the power of 2 and get 9.

$$sort(-54,2\times \frac{9}{4^{2}}+\frac{45}{2},16-\frac{72}{9})$$

Calculate 4 to the power of 2 and get 16.

$$sort(-54,2\times \frac{9}{16}+\frac{45}{2},16-\frac{72}{9})$$

Multiply 2 and \frac{9}{16} to get \frac{9}{8}.

$$sort(-54,\frac{9}{8}+\frac{45}{2},16-\frac{72}{9})$$

Add \frac{9}{8} and \frac{45}{2} to get \frac{189}{8}.

$$sort(-54,\frac{189}{8},16-\frac{72}{9})$$

Divide 72 by 9 to get 8.

$$sort(-54,\frac{189}{8},16-8)$$

Subtract 8 from 16 to get 8.

$$sort(-54,\frac{189}{8},8)$$

Convert decimal numbers in the list -54,\frac{189}{8},8 to fractions.

$$-54,\frac{189}{8},8$$

To sort the list, start from a single element -54.

$$-54$$

Insert \frac{189}{8} to the appropriate location in the new list.

$$-54,\frac{189}{8}$$

Insert 8 to the appropriate location in the new list.

$$-54,8,\frac{189}{8}$$

Evaluate

$$-54,\ \frac{189}{8},\ 8$$