Answer
a. $\sqrt4$
b. $0$ and $\sqrt4$
c. $-5, 0, \text{ and } \sqrt4$
d. $-5, -0.\overline{3}, 0, \sqrt4$
e. $\sqrt2$
f. $-5, -0.\overline{3}, 0, \sqrt2, \sqrt4$
Work Step by Step
(a) The natural numbers are the counting numbers $1, 2, 3, ...$
Thus, the only natural number in the given set is $\sqrt{4}$ since it is equal to $2$.
(b) The whole numbers are $0, 1, 2, 3, ...$
Thus, whole numbers in the given set are $0$ and $\sqrt{4}$.
(c) The integers are $..., -3, -2, -1, 0, 1, 2, 3, ...$
Thus, the integers in the given set are $-5, 0, \sqrt{4}$.
(d) Rational numbers are numbers that can be expressed as a fraction (or a quotient of two integers, where the denominator is not zero).
Thus, the rational numbers in the given set are $-5, -0.\overline{3}, 0, \sqrt{4}$.
(e) Irrational numbers are numbers that cannot be expressed as a fraction (or a quotient of two integers, where the denominator is not zero).
Thus, the only irrational number in the given set is $\sqrt2$.
(f) All the numbers in the set are real numbers.
