Solve sqrt{15^{2}-(8*9+3^{2}-11+4^2+2^2):10-(6^2-4^2)}

$$\sqrt { 15 ^ { 2 } - ( 8 \times 9 + 3 ^ { 2 } - 11 + 4 ^ { 2 } + 2 ^ { 2 } ) : 10 - ( 6 ^ { 2 } - 4 ^ { 2 } ) }$$

Evaluate

$$14$$

Solution Steps

Calculate 15 to the power of 2 and get 225.

$$\sqrt{225-\frac{8\times 9+3^{2}-11+4^{2}+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Multiply 8 and 9 to get 72.

$$\sqrt{225-\frac{72+3^{2}-11+4^{2}+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{225-\frac{72+9-11+4^{2}+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Add 72 and 9 to get 81.

$$\sqrt{225-\frac{81-11+4^{2}+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Subtract 11 from 81 to get 70.

$$\sqrt{225-\frac{70+4^{2}+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{225-\frac{70+16+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Add 70 and 16 to get 86.

$$\sqrt{225-\frac{86+2^{2}}{10}-\left(6^{2}-4^{2}\right)}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{225-\frac{86+4}{10}-\left(6^{2}-4^{2}\right)}$$

Add 86 and 4 to get 90.

$$\sqrt{225-\frac{90}{10}-\left(6^{2}-4^{2}\right)}$$

Divide 90 by 10 to get 9.

$$\sqrt{225-9-\left(6^{2}-4^{2}\right)}$$

Subtract 9 from 225 to get 216.

$$\sqrt{216-\left(6^{2}-4^{2}\right)}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{216-\left(36-4^{2}\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{216-\left(36-16\right)}$$

Subtract 16 from 36 to get 20.

$$\sqrt{216-20}$$

Subtract 20 from 216 to get 196.

$$\sqrt{196}$$

Calculate the square root of 196 and get 14.

$$14$$

Factor

$$2\times 7$$