Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals. $sqrt{-2}$

Explanation:

Step1: Rewrite negative radicand

$\sqrt{-2} = \sqrt{-1 \times 2}$

Step2: Split the square root

$\sqrt{-1 \times 2} = \sqrt{-1} \times \sqrt{2}$

Step3: Substitute $i = \sqrt{-1}$

$\sqrt{-1} \times \sqrt{2} = i\sqrt{2}$

Answer:

$i\sqrt{2}$