Solve sqrt{22+2sqrt{16}+2sqrt{64}+2sqrt{81}}

$$\sqrt { 22 + 2 \sqrt { 16 } + 2 \sqrt { 64 } + 2 \sqrt { 81 } }$$

Evaluate

$$8$$

Solution Steps

Calculate the square root of 16 and get 4.

$$\sqrt{22+2\times 4+2\sqrt{64}+2\sqrt{81}}$$

Multiply 2 and 4 to get 8.

$$\sqrt{22+8+2\sqrt{64}+2\sqrt{81}}$$

Add 22 and 8 to get 30.

$$\sqrt{30+2\sqrt{64}+2\sqrt{81}}$$

Calculate the square root of 64 and get 8.

$$\sqrt{30+2\times 8+2\sqrt{81}}$$

Multiply 2 and 8 to get 16.

$$\sqrt{30+16+2\sqrt{81}}$$

Add 30 and 16 to get 46.

$$\sqrt{46+2\sqrt{81}}$$

Calculate the square root of 81 and get 9.

$$\sqrt{46+2\times 9}$$

Multiply 2 and 9 to get 18.

$$\sqrt{46+18}$$

Add 46 and 18 to get 64.

$$\sqrt{64}$$

Calculate the square root of 64 and get 8.

$$8$$

Factor

$$2^{3}$$