Solve sigma/sqrt{(213369-283024)(167544-84(021)}

$$\frac { \sigma } { \sqrt { ( 213369 - 283024 ) ( 167544 - 84 ( 021 ) } }$$

Evaluate (complex solution)

$$-\frac{\sqrt{12830451}i\sigma }{384913530}$$

Solution Steps

Subtract 283024 from 213369 to get -69655.

$$\frac{\sigma }{\sqrt{-69655\left(167544-84\times 21\right)}}$$

Multiply 84 and 21 to get 1764.

$$\frac{\sigma }{\sqrt{-69655\left(167544-1764\right)}}$$

Subtract 1764 from 167544 to get 165780.

$$\frac{\sigma }{\sqrt{-69655\times 165780}}$$

Multiply -69655 and 165780 to get -11547405900.

$$\frac{\sigma }{\sqrt{-11547405900}}$$

Factor -11547405900=\left(30i\right)^{2}\times 12830451. Rewrite the square root of the product \sqrt{\left(30i\right)^{2}\times 12830451} as the product of square roots \sqrt{\left(30i\right)^{2}}\sqrt{12830451}. Take the square root of \left(30i\right)^{2}.

$$\frac{\sigma }{30i\sqrt{12830451}}$$

Rationalize the denominator of \frac{\sigma }{30i\sqrt{12830451}} by multiplying numerator and denominator by \sqrt{12830451}.

$$\frac{\sigma \sqrt{12830451}}{30i\left(\sqrt{12830451}\right)^{2}}$$

The square of \sqrt{12830451} is 12830451.

$$\frac{\sigma \sqrt{12830451}}{30i\times 12830451}$$

Multiply 30i and 12830451 to get 384913530i.

$$\frac{\sigma \sqrt{12830451}}{384913530i}$$

Evaluate

$$\text{Indeterminate}$$