Question

question
write $sqrt{-200}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Separate negative and positive terms

$\sqrt{-200} = \sqrt{-1 \times 200}$

Step2: Split the radical into two factors

$\sqrt{-1 \times 200} = \sqrt{-1} \times \sqrt{200}$

Step3: Simplify $\sqrt{-1}$ and factor 200

$\sqrt{-1}=i$, $\sqrt{200}=\sqrt{100 \times 2}$

Step4: Simplify $\sqrt{100 \times 2}$

$\sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}$

Step5: Combine the terms

$i \times 10\sqrt{2} = 10i\sqrt{2}$

Answer:

$10i\sqrt{2}$