No, \( \sqrt{200} \) is **not a rational number**.

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where both \( a \) and \( b \) are integers, and \( b \neq 0 \).

To explain this:

- \( \sqrt{200} = \sqrt{2^2 \times 5^2 \times 2} = 10\sqrt{2} \).
- Since \( \sqrt{2} \) is an **irrational number** (it cannot be expressed as a simple fraction), multiplying it by 10 still results in an irrational number.

Thus, \( \sqrt{200} \) cannot be expressed as a fraction and is, therefore, irrational.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the difference between rational and irrational numbers?
2. How can we simplify square roots, like \( \sqrt{200} \)?
3. What is the decimal approximation of \( \sqrt{200} \)?
4. Are all square roots of non-perfect squares irrational?
5. Can irrational numbers be expressed as repeating decimals?

**Tip:** Any square root of a non-perfect square will always be irrational.

Explore whether \( \sqrt{200} \) is a rational number with a detailed explanation. This problem highlights key number theory concepts such as square roots and irrational numbers. Suitable for students in Grades 8-10.

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