Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals. \\(-\sqrt{-50}\\)

Explanation:

Step1: Rewrite the radical

We know that $\sqrt{-a}=\sqrt{a}\cdot\sqrt{-1}$ for $a\geq0$. So, $-\sqrt{-50}=-\sqrt{50}\cdot\sqrt{-1}$.

Step2: Simplify $\sqrt{50}$

Factor 50: $50 = 25\times2$. Then $\sqrt{50}=\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}=5\sqrt{2}$.

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

Since $\sqrt{-1}=i$, we have $-\sqrt{50}\cdot\sqrt{-1}=-5\sqrt{2}\cdot i=-5i\sqrt{2}$.

Answer:

$-5i\sqrt{2}$