Which numbers are both integers and irrational numbers?
1) zero
2) none
3) negative integers - no response given
4) square roots of integers
2) none
The correct answer is 2) none.
Integers are whole numbers that can be positive, negative, or zero. Irrational numbers, on the other hand, cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
Zero (option 1) is an integer but not an irrational number because it can be expressed as the fraction 0/1.
Negative integers (option 3) are integers but not irrational numbers since they can be expressed as negative fractions.
Square roots of integers (option 4) can be either rational or irrational numbers. For example, the square root of 4 is 2, which is a rational number since it can be expressed as the fraction 2/1. However, the square root of 2 is irrational because it cannot be expressed as a fraction.
Therefore, the correct answer is 2) none.