which expression is equivalent to $sqrt{-80}$?\n- $-4sqrt{5}$\n- $-4isqrt{5}$\n- $4isqrt{5}$\n- $4sqrt{5}$

Explanation:

Step1: Rewrite -80 as a product

We know that (-80=-1\times16\times5). So, (\sqrt{-80}=\sqrt{-1\times16\times5}).

Step2: Use the property of square - roots (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b})

(\sqrt{-1\times16\times5}=\sqrt{-1}\times\sqrt{16}\times\sqrt{5}).

Step3: Recall the definition of the imaginary unit

Since (\sqrt{-1} = i) and (\sqrt{16}=4), then (\sqrt{-1}\times\sqrt{16}\times\sqrt{5}=i\times4\times\sqrt{5}=4i\sqrt{5}).

Answer:

C. (4i\sqrt{5})