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The image appears to ask: "The number \( x \) is natural. Which statement about \( \sqrt{x} \) is true?"

The answer choices seem to be:
1. \( \sqrt{x} \) is rational.
2. \( \sqrt{x} \) is irrational.
3. \( \sqrt{x} \) can be rational or irrational depending on the value of \( x \).

Since \( x \) is a natural number, the square root \( \sqrt{x} \) will be rational only if \( x \) is a perfect square (e.g., \( x = 1, 4, 9, 16, \ldots \)). For non-perfect squares, \( \sqrt{x} \) will be irrational.

Thus, the correct answer is:
**3. \( \sqrt{x} \) can be rational or irrational depending on the value of \( x \)**.

Would you like any further details on this, or do you have other questions?

Here are 5 related questions to expand on this concept:
1. What is the definition of a natural number?
2. What makes a number rational or irrational?
3. Can a square root of a non-perfect square ever be rational?
4. How can you determine if a number is a perfect square?
5. How does the square root function behave for very large natural numbers?

**Tip**: A rational number is any number that can be expressed as a fraction of two integers, while an irrational number cannot be written in such a form.

The number x is natural. Which statement about \( \sqrt{x} \) is true?

Learn how to determine whether the square root of a natural number is rational or irrational. This explanation covers the key concepts of perfect squares and irrational numbers. Suitable for students in Grades 8-10.

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