What type of numbers are whole numbers with square roots that are decimals and do not repeat?

• A. Whole numbers
• B. Irrational numbers
• C. Rational numbers
• D. Integer numbers

Answer: (B)

The question is asking about a specific category of numbers where whole numbers have square roots that result in decimal values that do not repeat.

When we consider square roots, many whole numbers yield square roots that are either whole numbers themselves (like the square root of 1, which is 1, or the square root of 4, which is 2) or numbers that are not whole, such as the square root of 2. The square root of 2 is approximately 1.414213..., and this decimal representation does not repeat and does not terminate.

This characteristic identifies square roots like that of 2, 3, 5, and other non-perfect square whole numbers as irrational numbers. An irrational number is defined as any number that cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers and has a decimal representation that neither repeats nor terminates.

In contrast, whole numbers are integers that are non-negative (0, 1, 2, 3, etc.), and they do not include decimals or negative numbers. Rational numbers are those that can be represented as the fraction of two integers, including whole numbers, integers, and numbers like 0.5 (which is