Solve fsqrt{-2}*sqrt{8}?

$$f \sqrt { - 2 } \cdot \sqrt { 8 } ?$$

Evaluate (complex solution)

$$4if$$

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.

$$f\sqrt{2}i\sqrt{8}$$

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}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$f\times 2\times \left(2i\right)$$

Multiply 2 and 2i to get 4i.

$$f\times \left(4i\right)$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

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}.

$$f\sqrt{-2}\times 2\sqrt{2}$$