Which numbers are both integers and irrational numbers? (1 point)
• none
• zero
• negative integers
.square roots of integers
none
The numbers that are both integers and irrational numbers are none of the options provided.
To determine which numbers are both integers and irrational, we need to understand the definitions of integers and irrational numbers.
Integers are numbers that belong to the set of whole numbers, including positive, negative, and zero. They have no fractional or decimal parts. Examples of integers are -3, 0, and 5.
On the other hand, irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. They have non-repeating and non-terminating decimal representations. Common examples of irrational numbers include √2, π (pi), and e.
Now, let's consider each option:
• None: This option suggests that there are no numbers that are both integers and irrational. It is correct since integers are rational by definition, meaning they can be expressed as a ratio of two integers. Therefore, none of them are irrational.
• Zero: Zero is an integer, but it is not an irrational number. It can be written as the ratio 0/1, which makes it a rational number.
• Negative integers: Negative integers are integers, but they are not irrational numbers. Like positive integers, negative integers can be expressed as a ratio of two integers, making them rational.
• Square roots of integers: The square roots of integers can sometimes be irrational numbers. For example, √2 is an irrational number, since it cannot be expressed as a fraction or a ratio of two integers. However, not all square roots of integers are irrational. The square root of a perfect square integer, such as √4 (which equals 2) or √9 (which equals 3), are actually integers.
Therefore, the correct answer is: the square roots of integers. Some square roots of integers are irrational numbers.