Solve sqrt{9+4sqrt{36-2sqrt{6^2+8^2}}}=?

$$\sqrt { 9 + 4 \sqrt { 36 - 2 \sqrt { 6 ^ { 2 } + 8 ^ { 2 } } } } = ?$$

Evaluate

$$5$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{9+4\sqrt{36-2\sqrt{36+8^{2}}}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{9+4\sqrt{36-2\sqrt{36+64}}}$$

Add 36 and 64 to get 100.

$$\sqrt{9+4\sqrt{36-2\sqrt{100}}}$$

Calculate the square root of 100 and get 10.

$$\sqrt{9+4\sqrt{36-2\times 10}}$$

Multiply 2 and 10 to get 20.

$$\sqrt{9+4\sqrt{36-20}}$$

Subtract 20 from 36 to get 16.

$$\sqrt{9+4\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\sqrt{9+4\times 4}$$

Multiply 4 and 4 to get 16.

$$\sqrt{9+16}$$

Add 9 and 16 to get 25.

$$\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$5$$

Factor

$$5$$