Question

Which numbers are both integers and irrational numbers?
A. Square root of integers
B. Negative numbers
C. Zero
D. None

Answer 1

To determine which numbers are both integers and irrational numbers, we need to understand the definitions of these terms:

- **Integers** are whole numbers that can be positive, negative, or zero. Examples include -2, -1, 0, 1, 2, etc.

- **Irrational numbers** are real numbers that cannot be expressed as a fraction of two integers. They cannot be written in the form \( p/q \) where \( p \) and \( q \) are integers (with \( q \neq 0 \)). Common examples include numbers such as \(\sqrt{2}\), \(\pi\), and \(e\).

Now let's analyze the options:

A. **Square root of integers**: The square root of an integer can be either an integer or an irrational number. For example, \(\sqrt{4} = 2\) (which is an integer) and \(\sqrt{2}\) (which is irrational).

B. **Negative numbers**: Negative numbers can only be integers or rational numbers. There are no negative irrational numbers that are also integers.

C. **Zero**: Zero is an integer, and it is neither rational nor irrational. It can be expressed as \(0/1\) (therefore it is rational).

D. **None**: This means there would be no options that satisfy the criteria of being both integers and irrational numbers.

Given these definitions, we see that integers cannot be irrational since all integers are rational (they can be expressed in a simple fraction form). Therefore, the answer is:

**D. None**.