Question

simplify √(-50). 5√2 5i√2 -5√2 -5i√2

Explanation:

Step1: Rewrite -50 as product

We know that $-50=-1\times50$. So, $\sqrt{-50}=\sqrt{-1\times50}$.

Step2: Use square - root property

By the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (where $a = - 1$ and $b = 50$), we have $\sqrt{-1\times50}=\sqrt{-1}\cdot\sqrt{50}$.

Step3: Simplify $\sqrt{-1}$ and $\sqrt{50}$

We know that $\sqrt{-1}=i$, and $\sqrt{50}=\sqrt{25\times2}=\sqrt{25}\cdot\sqrt{2}=5\sqrt{2}$.

Step4: Combine the results

So, $\sqrt{-1}\cdot\sqrt{50}=i\times5\sqrt{2}=5i\sqrt{2}$.

Answer:

$5i\sqrt{2}$