Solve {l}{sqrt{sqrt{81}}}{sqrt{100/25}}{sqrt[3]{sqrt{729}}}{sqrt{sqrt[4]{256}}}{sqrt[5]{8^5}}{sqrt{64}*81*100}{36/36}

$$\left. \begin{array} { l } { \sqrt { \sqrt { 81 } } } \\ { \sqrt { \frac { 100 } { 25 } } } \\ { \sqrt[ 3 ] { \sqrt { 729 } } } \\ { \sqrt { \sqrt[ 4 ] { 256 } } } \\ { \sqrt[ 5 ] { 8 ^ { 5 } } } \\ { \sqrt { 64 } \times 81 \times 100 } \\ { \frac { 36 } { 36 } } \end{array} \right.$$

Sort

$$1,2,2,3,3,8,64800$$

Solution Steps

Divide 36 by 36 to get 1.

$$sort(\sqrt{\sqrt{81}},\sqrt{\frac{100}{25}},\sqrt[3]{\sqrt{729}},\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate the square root of 81 and get 9.

$$sort(\sqrt{9},\sqrt{\frac{100}{25}},\sqrt[3]{\sqrt{729}},\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate the square root of 9 and get 3.

$$sort(3,\sqrt{\frac{100}{25}},\sqrt[3]{\sqrt{729}},\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Divide 100 by 25 to get 4.

$$sort(3,\sqrt{4},\sqrt[3]{\sqrt{729}},\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate the square root of 4 and get 2.

$$sort(3,2,\sqrt[3]{\sqrt{729}},\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate the square root of 729 and get 27.

$$sort(3,2,\sqrt[3]{27},\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

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

$$sort(3,2,3,\sqrt{\sqrt[4]{256}},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate \sqrt[4]{256} and get 4.

$$sort(3,2,3,\sqrt{4},\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate the square root of 4 and get 2.

$$sort(3,2,3,2,\sqrt[5]{8^{5}},\sqrt{64}\times 81\times 100,1)$$

Calculate 8 to the power of 5 and get 32768.

$$sort(3,2,3,2,\sqrt[5]{32768},\sqrt{64}\times 81\times 100,1)$$

Calculate \sqrt[5]{32768} and get 8.

$$sort(3,2,3,2,8,\sqrt{64}\times 81\times 100,1)$$

Calculate the square root of 64 and get 8.

$$sort(3,2,3,2,8,8\times 81\times 100,1)$$

Multiply 8 and 81 to get 648.

$$sort(3,2,3,2,8,648\times 100,1)$$

Multiply 648 and 100 to get 64800.

$$sort(3,2,3,2,8,64800,1)$$

To sort the list, start from a single element 3.

$$3$$

Insert 2 to the appropriate location in the new list.

$$2,3$$

Insert 3 to the appropriate location in the new list.

$$2,3,3$$

Insert 2 to the appropriate location in the new list.

$$2,2,3,3$$

Insert 8 to the appropriate location in the new list.

$$2,2,3,3,8$$

Insert 64800 to the appropriate location in the new list.

$$2,2,3,3,8,64800$$

Insert 1 to the appropriate location in the new list.

$$1,2,2,3,3,8,64800$$

Evaluate

$$3,\ 2,\ 3,\ 2,\ 8,\ 64800,\ 1$$