Solve sqrt{sqrt{1+4+sqrt{121}}-15^2:5^2:3}=

$$\sqrt { \sqrt { 1 + 4 + \sqrt { 121 } } - 15 ^ { 2 } : 5 ^ { 2 } : 3 } =$$

Evaluate

$$1$$

Solution Steps

Add 1 and 4 to get 5.

$$\sqrt{\sqrt{5+\sqrt{121}}-\frac{\frac{15^{2}}{5^{2}}}{3}}$$

Calculate the square root of 121 and get 11.

$$\sqrt{\sqrt{5+11}-\frac{\frac{15^{2}}{5^{2}}}{3}}$$

Add 5 and 11 to get 16.

$$\sqrt{\sqrt{16}-\frac{\frac{15^{2}}{5^{2}}}{3}}$$

Calculate the square root of 16 and get 4.

$$\sqrt{4-\frac{\frac{15^{2}}{5^{2}}}{3}}$$

Express \frac{\frac{15^{2}}{5^{2}}}{3} as a single fraction.

$$\sqrt{4-\frac{15^{2}}{5^{2}\times 3}}$$

Calculate 15 to the power of 2 and get 225.

$$\sqrt{4-\frac{225}{5^{2}\times 3}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{4-\frac{225}{25\times 3}}$$

Multiply 25 and 3 to get 75.

$$\sqrt{4-\frac{225}{75}}$$

Divide 225 by 75 to get 3.

$$\sqrt{4-3}$$

Subtract 3 from 4 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$