Solve sqrt{-2}+sqrt{-8}

$$\sqrt { - 2 } + \sqrt { - 8 }$$

Evaluate (complex solution)

$$3\sqrt{2}i\approx 4.242640687i$$

Solution Steps

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.

$$\sqrt{2}i+\sqrt{-8}$$

Factor -8=\left(2i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 2} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{2}. Take the square root of \left(2i\right)^{2}.

$$\sqrt{2}i+2i\sqrt{2}$$

Combine \sqrt{2}i and 2i\sqrt{2} to get 3i\sqrt{2}.

$$3i\sqrt{2}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$