Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals.
$1 + \sqrt{-24}$

Explanation:

Step1: Rewrite sqrt(-24) using i

Recall that $\sqrt{-a} = i\sqrt{a}$ for $a>0$, so $\sqrt{-24} = i\sqrt{24}$

Step2: Simplify sqrt(24)

Factor 24 into $4\times6$, so $\sqrt{24} = \sqrt{4\times6} = \sqrt{4}\times\sqrt{6} = 2\sqrt{6}$

Step3: Combine terms

Substitute back to the original expression: $1 + i\times2\sqrt{6}$

Answer:

$1 + 2i\sqrt{6}$