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The question is asking which set(s) of numbers \(-\sqrt{25}\) belongs to, where \(\sqrt{25} = 5\). Hence, \(-\sqrt{25} = -5\).

Let’s analyze the sets of numbers:

1. **Natural Numbers (I)**: Natural numbers are positive whole numbers (1, 2, 3, ...). \(-5\) is not a natural number.
2. **Integer (II)**: Integers include all whole numbers, both positive and negative. \(-5\) is an integer.
3. **Rational (III)**: Rational numbers are numbers that can be expressed as a fraction of two integers. \(-5\) can be written as \(-5/1\), so it is a rational number.
4. **Irrational (IV)**: Irrational numbers cannot be written as a simple fraction. \(-5\) is not an irrational number.

Thus, \(-\sqrt{25} = -5\) belongs to **sets II and III** (Integers and Rational numbers).

The correct answer is **c. II and III only**.

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. What is the difference between rational and irrational numbers?
2. Can negative numbers ever be considered natural numbers?
3. How do we determine if a square root is rational or irrational?
4. What are examples of numbers belonging to all four sets: natural, integer, rational, and irrational?
5. How does \(-\sqrt{25}\) differ from \(\sqrt{-25}\)?

**Tip**: Remember, a rational number is any number that can be written as a fraction, and integers are simply rational numbers with a denominator of 1!

To which set(s) of numbers does -√25 belong?

Learn how to classify -√25 into different number sets such as integers and rational numbers. This problem covers square roots and the properties of natural, integer, rational, and irrational numbers. Suitable for students in Grades 6-8.

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