Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals.
$13 - \sqrt{-46}$

Explanation:

Step1: Rewrite negative radical

Recall that $\sqrt{-a} = i\sqrt{a}$ for $a>0$. So $\sqrt{-46} = i\sqrt{46}$.

Step2: Substitute back to expression

Replace $\sqrt{-46}$ in the original expression.
$13 - \sqrt{-46} = 13 - i\sqrt{46}$

Answer:

$13 - i\sqrt{46}$