Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals.
$13 + \sqrt{-8}$

Explanation:

Step1: Rewrite negative radical

$\sqrt{-8} = \sqrt{8 \times (-1)}$

Step2: Separate into real and imaginary parts

$\sqrt{8 \times (-1)} = \sqrt{8} \times \sqrt{-1}$

Step3: Simplify radical and substitute $i=\sqrt{-1}$

$\sqrt{8} = 2\sqrt{2}$, so $\sqrt{-8}=2\sqrt{2}i$

Step4: Combine with real term

$13 + 2\sqrt{2}i$

Answer:

$13 + 2\sqrt{2}i$