Solve sqrt{sqrt{16}*9^2-sqrt{289}}+[sqrt{144}:12]+4^2

$$\sqrt { \sqrt { 16 } \times 9 ^ { 2 } - \sqrt { 289 } } + [ \sqrt { 144 } : 12 ] + 4 ^ { 2 }$$

Evaluate

$$\sqrt{307}+17\approx 34.521415468$$

Solution Steps

Calculate the square root of 16 and get 4.

$$\sqrt{4\times 9^{2}-\sqrt{289}}+\frac{\sqrt{144}}{12}+4^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{4\times 81-\sqrt{289}}+\frac{\sqrt{144}}{12}+4^{2}$$

Multiply 4 and 81 to get 324.

$$\sqrt{324-\sqrt{289}}+\frac{\sqrt{144}}{12}+4^{2}$$

Calculate the square root of 289 and get 17.

$$\sqrt{324-17}+\frac{\sqrt{144}}{12}+4^{2}$$

Subtract 17 from 324 to get 307.

$$\sqrt{307}+\frac{\sqrt{144}}{12}+4^{2}$$

Calculate the square root of 144 and get 12.

$$\sqrt{307}+\frac{12}{12}+4^{2}$$

Divide 12 by 12 to get 1.

$$\sqrt{307}+1+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{307}+1+16$$

Add 1 and 16 to get 17.

$$\sqrt{307}+17$$

Factor

$$\sqrt{307} + 17 = 34.521415468$$