Write square root of, minus, 200, end square root 
−200
​
  in simplest radical form.

The expression you're trying to simplify is:

\[
\sqrt{-200}
\]

Since the square root of a negative number involves imaginary numbers, we can rewrite the square root of a negative number using the imaginary unit \( i \), where \( i = \sqrt{-1} \).

First, let's separate the negative sign:

\[
\sqrt{-200} = \sqrt{-1} \times \sqrt{200} = i \times \sqrt{200}
\]

Next, simplify \( \sqrt{200} \). We can break down 200 into its prime factors:

\[
200 = 2^3 \times 5^2
\]

The square root of 200 is:

\[
\sqrt{200} = \sqrt{2^3 \times 5^2} = \sqrt{2^2 \times 5^2 \times 2} = 10\sqrt{2}
\]

So, the simplified form of \( \sqrt{-200} \) is:

\[
\sqrt{-200} = 10i\sqrt{2}
\]

Thus, the simplest radical form of \( \sqrt{-200} \) is:

\[
10i\sqrt{2}
\]

Would you like a detailed breakdown of this process?

Here are some related questions to explore:
1. How do you simplify square roots involving negative numbers?
2. What is the meaning of the imaginary unit \( i \)?
3. How do you factor numbers to simplify square roots?
4. Can you explain the concept of imaginary and complex numbers?
5. How does \( i \) behave in more complex operations like powers?

**Tip:** Always check for perfect squares within the radicand to simplify square roots easily.

Write square root of, minus, 200, end square root (−200) in simplest radical form.

Learn how to simplify the square root of -200, involving imaginary numbers and radicals. This step-by-step solution demonstrates the process of using the imaginary unit \( i \) and simplifying square roots with prime factorization. Perfect for Grades 9-11 students.

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