Solve frac{sqrt{-16}}{sqrt{-2}}

$$\frac { \sqrt { - 16 } } { \sqrt { - 2 } }$$

Evaluate (complex solution)

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Calculate the square root of -16 and get 4i.

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

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

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

Rationalize the denominator of \frac{4i}{\sqrt{2}i} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4i\sqrt{2}}{\left(\sqrt{2}\right)^{2}i}$$

The square of \sqrt{2} is 2.

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

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

$$2\sqrt{2}$$

Real Part (complex solution)

$$2 \sqrt{2} = 2.828427125$$

Evaluate

$$\text{Indeterminate}$$