Solve 12sqrt{2/3-25}

$$12 \sqrt{ \frac{ 2 }{ 3-25 } }$$

Evaluate (complex solution)

$$\frac{12\sqrt{11}i}{11}\approx 3.618136135i$$

Solution Steps

Subtract 25 from 3 to get -22.

$$12\sqrt{\frac{2}{-22}}$$

Reduce the fraction \frac{2}{-22} to lowest terms by extracting and canceling out 2.

$$12\sqrt{-\frac{1}{11}}$$

Rewrite the square root of the division \sqrt{-\frac{1}{11}} as the division of square roots \frac{\sqrt{-1}}{\sqrt{11}}.

$$12\times \frac{\sqrt{-1}}{\sqrt{11}}$$

Calculate the square root of -1 and get i.

$$12\times \frac{i}{\sqrt{11}}$$

Rationalize the denominator of \frac{i}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$12\times \frac{i\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$12\times \frac{i\sqrt{11}}{11}$$

Divide i\sqrt{11} by 11 to get \frac{1}{11}i\sqrt{11}.

$$12\times \left(\frac{1}{11}i\right)\sqrt{11}$$

Multiply 12 and \frac{1}{11}i to get \frac{12}{11}i.

$$\frac{12}{11}i\sqrt{11}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$