Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals.
$-sqrt{-52}$

Explanation:

Step1: Rewrite the radical

We know that $\sqrt{-a}=\sqrt{a}\cdot\sqrt{-1}$ for $a\geq0$. So, $-\sqrt{-52}=-\sqrt{52}\cdot\sqrt{-1}$.

Step2: Simplify $\sqrt{52}$

Factor 52: $52 = 4\times13$. Then $\sqrt{52}=\sqrt{4\times13}=\sqrt{4}\times\sqrt{13}=2\sqrt{13}$.

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

Since $\sqrt{-1}=i$, we have $-\sqrt{52}\cdot\sqrt{-1}=-2\sqrt{13}\cdot i=-2i\sqrt{13}$.

Answer:

$-2i\sqrt{13}$