Question

what number is equivalent to \\(sqrt{-8} cdot sqrt{-32}\\)? \\(\text{a}\\) 16 \\(\text{b}\\) -16 \\(\text{c}\\) \\(-8sqrt{2}\\) \\(\text{d}\\) \\(8sqrt{2}\\)

Explanation:

Step1: Rewrite with imaginary unit $i$

$\sqrt{-8} = i\sqrt{8}$, $\sqrt{-32}=i\sqrt{32}$

Step2: Multiply the two expressions

$i\sqrt{8} \cdot i\sqrt{32} = i^2 \cdot \sqrt{8 \times 32}$

Step3: Simplify $i^2$ and product inside root

$i^2=-1$, $\sqrt{8 \times 32}=\sqrt{256}=16$

Step4: Calculate final value

$-1 \times 16 = -16$

Answer:

B. -16