Solve sqrt{5-sqrt{9+sqrt{2^2*10+3^2}}}

$$\sqrt { 5 - \sqrt { 9 + \sqrt { 2 ^ { 2 } \cdot 10 + 3 ^ { 2 } } } }$$

Evaluate

$$1$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\sqrt{5-\sqrt{9+\sqrt{4\times 10+3^{2}}}}$$

Multiply 4 and 10 to get 40.

$$\sqrt{5-\sqrt{9+\sqrt{40+3^{2}}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{5-\sqrt{9+\sqrt{40+9}}}$$

Add 40 and 9 to get 49.

$$\sqrt{5-\sqrt{9+\sqrt{49}}}$$

Calculate the square root of 49 and get 7.

$$\sqrt{5-\sqrt{9+7}}$$

Add 9 and 7 to get 16.

$$\sqrt{5-\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\sqrt{5-4}$$

Subtract 4 from 5 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$