Solve sqrt{-1/8}

$$\sqrt { - \frac { 1 } { 8 } }$$

Evaluate (complex solution)

$$\frac{\sqrt{2}i}{4}\approx 0.353553391i$$

Solution Steps

Rewrite the square root of the division \sqrt{-\frac{1}{8}} as the division of square roots \frac{\sqrt{-1}}{\sqrt{8}}.

$$\frac{\sqrt{-1}}{\sqrt{8}}$$

Calculate the square root of -1 and get i.

$$\frac{i}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{i}{2\sqrt{2}}$$

Rationalize the denominator of \frac{i}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{i\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{i\sqrt{2}}{4}$$

Divide i\sqrt{2} by 4 to get \frac{1}{4}i\sqrt{2}.

$$\frac{1}{4}i\sqrt{2}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$