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The problem asks about the rationality of the expression \( s - \sqrt{3} \), where \( s \) is a rational number.

Let's break this down:

- A **rational number** is any number that can be expressed as a fraction of two integers (like \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)).
- An **irrational number** cannot be expressed as such a fraction (like \( \sqrt{3} \), which has a non-repeating, non-terminating decimal expansion).

Now, let's consider the expression \( s - \sqrt{3} \):
1. \( s \) is rational.
2. \( \sqrt{3} \) is irrational.

When you subtract an irrational number (like \( \sqrt{3} \)) from a rational number (like \( s \)), the result is always irrational. This is because subtracting (or adding) an irrational number to a rational number will never yield a rational result.

Therefore, the correct answer is:  
**\( s - \sqrt{3} \) is irrational.**

Would you like any more details, or have any further questions?

Here are five related questions to consider:
1. What happens when you add two irrational numbers? Can the result ever be rational?
2. How can you prove that \( \sqrt{3} \) is irrational?
3. Is the sum of two rational numbers always rational?
4. What is the difference between algebraic and transcendental irrational numbers?
5. Can the product of a rational and an irrational number be rational?

**Tip:** Whenever you perform arithmetic operations involving irrational numbers, the outcome often remains irrational unless there's some special cancellation occurring!

The number s is rational. Which statement about s - sqrt(3) is true?

Learn how to determine whether the expression s - sqrt(3), where s is a rational number, results in a rational or irrational number. This problem covers core concepts of rational and irrational numbers and is suitable for Grades 8-10 students.

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