Solve sqrt{-1^2/3}

$$\sqrt{ - \frac{ { 1 }^{ 2 } }{ 3 } }$$

Evaluate (complex solution)

$$\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\sqrt{-\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{-\frac{1}{3}} as the division of square roots \frac{\sqrt{-1}}{\sqrt{3}}.

$$\frac{\sqrt{-1}}{\sqrt{3}}$$

Calculate the square root of -1 and get i.

$$\frac{i}{\sqrt{3}}$$

Rationalize the denominator of \frac{i}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{i\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{i\sqrt{3}}{3}$$

Divide i\sqrt{3} by 3 to get \frac{1}{3}i\sqrt{3}.

$$\frac{1}{3}i\sqrt{3}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$