Solve {l}{sqrt{51+2^{2}+3^{2}}-sqrt{3^{2}+4^{2}}+sqrt{6^2+3^3+1^4}}{sqrt{5*4+2*3-1}:sqrt{6*4-9*2-5}+sqrt{3^2}}

$$\left. \begin{array} { l } { \sqrt { 51 + 2 ^ { 2 } + 3 ^ { 2 } } - \sqrt { 3 ^ { 2 } + 4 ^ { 2 } } + \sqrt { 6 ^ { 2 } + 3 ^ { 3 } + 1 ^ { 4 } } } \\ { \sqrt { 5 \cdot 4 + 2 \cdot 3 - 1 } : \sqrt { 6 \cdot 4 - 9 \cdot 2 - 5 } + \sqrt { 3 ^ { 2 } } } \end{array} \right.$$

Sort

$$8,11$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$sort(\sqrt{51+4+3^{2}}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 51 and 4 to get 55.

$$sort(\sqrt{55+3^{2}}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate 3 to the power of 2 and get 9.

$$sort(\sqrt{55+9}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 55 and 9 to get 64.

$$sort(\sqrt{64}-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate the square root of 64 and get 8.

$$sort(8-\sqrt{3^{2}+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate 3 to the power of 2 and get 9.

$$sort(8-\sqrt{9+4^{2}}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate 4 to the power of 2 and get 16.

$$sort(8-\sqrt{9+16}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 9 and 16 to get 25.

$$sort(8-\sqrt{25}+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate the square root of 25 and get 5.

$$sort(8-5+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Subtract 5 from 8 to get 3.

$$sort(3+\sqrt{6^{2}+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate 6 to the power of 2 and get 36.

$$sort(3+\sqrt{36+3^{3}+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate 3 to the power of 3 and get 27.

$$sort(3+\sqrt{36+27+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 36 and 27 to get 63.

$$sort(3+\sqrt{63+1^{4}},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate 1 to the power of 4 and get 1.

$$sort(3+\sqrt{63+1},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 63 and 1 to get 64.

$$sort(3+\sqrt{64},\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate the square root of 64 and get 8.

$$sort(3+8,\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 3 and 8 to get 11.

$$sort(11,\frac{\sqrt{5\times 4+2\times 3-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Multiply 5 and 4 to get 20. Multiply 2 and 3 to get 6.

$$sort(11,\frac{\sqrt{20+6-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Add 20 and 6 to get 26.

$$sort(11,\frac{\sqrt{26-1}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Subtract 1 from 26 to get 25.

$$sort(11,\frac{\sqrt{25}}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Calculate the square root of 25 and get 5.

$$sort(11,\frac{5}{\sqrt{6\times 4-9\times 2-5}}+\sqrt{3^{2}})$$

Multiply 6 and 4 to get 24.

$$sort(11,\frac{5}{\sqrt{24-9\times 2-5}}+\sqrt{3^{2}})$$

Multiply 9 and 2 to get 18.

$$sort(11,\frac{5}{\sqrt{24-18-5}}+\sqrt{3^{2}})$$

Subtract 18 from 24 to get 6.

$$sort(11,\frac{5}{\sqrt{6-5}}+\sqrt{3^{2}})$$

Subtract 5 from 6 to get 1.

$$sort(11,\frac{5}{\sqrt{1}}+\sqrt{3^{2}})$$

Calculate the square root of 1 and get 1.

$$sort(11,\frac{5}{1}+\sqrt{3^{2}})$$

Anything divided by one gives itself.

$$sort(11,5+\sqrt{3^{2}})$$

Calculate 3 to the power of 2 and get 9.

$$sort(11,5+\sqrt{9})$$

Calculate the square root of 9 and get 3.

$$sort(11,5+3)$$

Add 5 and 3 to get 8.

$$sort(11,8)$$

To sort the list, start from a single element 11.

$$11$$

Insert 8 to the appropriate location in the new list.

$$8,11$$

Evaluate

$$11,\ 8$$