Question

which expression is equal to 2\sqrt{-32}?
-8i\sqrt{2}
8i\sqrt{2}
8\sqrt{2i}
-8\sqrt{2}

Explanation:

Step1: Rewrite -32 as -1×32

$2\sqrt{-32}=2\sqrt{-1\times32}$

Step2: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = - 1$, $b = 32$)

$2\sqrt{-1\times32}=2\sqrt{-1}\cdot\sqrt{32}$

Step3: Recall that $\sqrt{-1}=i$ and simplify $\sqrt{32}$

Since $\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$ and $\sqrt{-1}=i$, then $2\sqrt{-1}\cdot\sqrt{32}=2i\times4\sqrt{2}$

Step4: Multiply the coefficients

$2i\times4\sqrt{2}=8i\sqrt{2}$

Answer:

$8i\sqrt{2}$