Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals. \\(sqrt{-28}\\)

Explanation:

Step1: Rewrite the radical

We know that $\sqrt{-a}=\sqrt{a}\cdot\sqrt{-1}$ for $a\geq0$. So for $\sqrt{-28}$, we can rewrite it as $\sqrt{28}\cdot\sqrt{-1}$.

Step2: Simplify $\sqrt{28}$

Factor 28: $28 = 4\times7$. Then $\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}$.

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

Since $\sqrt{-1}=i$, we substitute it into the expression. So $\sqrt{28}\cdot\sqrt{-1}=2\sqrt{7}\cdot i = 2i\sqrt{7}$.

Answer:

$2i\sqrt{7}$