Solve {l}{sqrt{64}-(27:4+24:6)+2^3-3}{sqrt{64}-(7+4)+2^3-3}

$$\left. \begin{array} { l } { \sqrt { 64 } - ( 27 : 4 + 24 : 6 ) + 2 ^ { 3 } - 3 } \\ { \sqrt { 64 } - ( 7 + 4 ) + 2 ^ { 3 } - 3 } \end{array} \right.$$

Sort

$$2,\frac{9}{4}$$

Solution Steps

Calculate the square root of 64 and get 8.

$$sort(8-\left(\frac{27}{4}+\frac{24}{6}\right)+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Divide 24 by 6 to get 4.

$$sort(8-\left(\frac{27}{4}+4\right)+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Convert 4 to fraction \frac{16}{4}.

$$sort(8-\left(\frac{27}{4}+\frac{16}{4}\right)+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Since \frac{27}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$sort(8-\frac{27+16}{4}+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Add 27 and 16 to get 43.

$$sort(8-\frac{43}{4}+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Convert 8 to fraction \frac{32}{4}.

$$sort(\frac{32}{4}-\frac{43}{4}+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Since \frac{32}{4} and \frac{43}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{32-43}{4}+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Subtract 43 from 32 to get -11.

$$sort(-\frac{11}{4}+2^{3}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Calculate 2 to the power of 3 and get 8.

$$sort(-\frac{11}{4}+8-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Convert 8 to fraction \frac{32}{4}.

$$sort(-\frac{11}{4}+\frac{32}{4}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Since -\frac{11}{4} and \frac{32}{4} have the same denominator, add them by adding their numerators.

$$sort(\frac{-11+32}{4}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Add -11 and 32 to get 21.

$$sort(\frac{21}{4}-3,\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Convert 3 to fraction \frac{12}{4}.

$$sort(\frac{21}{4}-\frac{12}{4},\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Since \frac{21}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{21-12}{4},\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Subtract 12 from 21 to get 9.

$$sort(\frac{9}{4},\sqrt{64}-\left(7+4\right)+2^{3}-3)$$

Calculate the square root of 64 and get 8.

$$sort(\frac{9}{4},8-\left(7+4\right)+2^{3}-3)$$

Add 7 and 4 to get 11.

$$sort(\frac{9}{4},8-11+2^{3}-3)$$

Subtract 11 from 8 to get -3.

$$sort(\frac{9}{4},-3+2^{3}-3)$$

Calculate 2 to the power of 3 and get 8.

$$sort(\frac{9}{4},-3+8-3)$$

Add -3 and 8 to get 5.

$$sort(\frac{9}{4},5-3)$$

Subtract 3 from 5 to get 2.

$$sort(\frac{9}{4},2)$$

Convert decimal numbers in the list \frac{9}{4},2 to fractions.

$$\frac{9}{4},2$$

To sort the list, start from a single element \frac{9}{4}.

$$\frac{9}{4}$$

Insert 2 to the appropriate location in the new list.

$$2,\frac{9}{4}$$

Evaluate

$$\frac{9}{4},\ 2$$