Solve sqrt{[(13)^{2}-(07)^{2}+32]^2:11^2*5+[(28)^2-023]*10^2}

$$\sqrt { [ ( 13 ) ^ { 2 } - ( 07 ) ^ { 2 } + 32 ] ^ { 2 } : 11 ^ { 2 } \cdot 5 + [ ( 28 ) ^ { 2 } - 023 ] \cdot 10 ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{9688405}}{11}\approx 282.965479891$$

Solution Steps

Calculate 13 to the power of 2 and get 169.

$$\sqrt{\frac{\left(169-\left(0\times 7\right)^{2}+32\right)^{2}}{11^{2}}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Multiply 0 and 7 to get 0.

$$\sqrt{\frac{\left(169-0^{2}+32\right)^{2}}{11^{2}}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$\sqrt{\frac{\left(169-0+32\right)^{2}}{11^{2}}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Subtract 0 from 169 to get 169.

$$\sqrt{\frac{\left(169+32\right)^{2}}{11^{2}}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Add 169 and 32 to get 201.

$$\sqrt{\frac{201^{2}}{11^{2}}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Calculate 201 to the power of 2 and get 40401.

$$\sqrt{\frac{40401}{11^{2}}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Calculate 11 to the power of 2 and get 121.

$$\sqrt{\frac{40401}{121}\times 5+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Multiply \frac{40401}{121} and 5 to get \frac{202005}{121}.

$$\sqrt{\frac{202005}{121}+\left(28^{2}-0\times 23\right)\times 10^{2}}$$

Calculate 28 to the power of 2 and get 784.

$$\sqrt{\frac{202005}{121}+\left(784-0\times 23\right)\times 10^{2}}$$

Multiply 0 and 23 to get 0.

$$\sqrt{\frac{202005}{121}+\left(784-0\right)\times 10^{2}}$$

Subtract 0 from 784 to get 784.

$$\sqrt{\frac{202005}{121}+784\times 10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{202005}{121}+784\times 100}$$

Multiply 784 and 100 to get 78400.

$$\sqrt{\frac{202005}{121}+78400}$$

Add \frac{202005}{121} and 78400 to get \frac{9688405}{121}.

$$\sqrt{\frac{9688405}{121}}$$

Rewrite the square root of the division \sqrt{\frac{9688405}{121}} as the division of square roots \frac{\sqrt{9688405}}{\sqrt{121}}.

$$\frac{\sqrt{9688405}}{\sqrt{121}}$$

Calculate the square root of 121 and get 11.

$$\frac{\sqrt{9688405}}{11}$$