Answer
a. Natural: $\sqrt{4}$
b. Whole: $0,\sqrt{4}$
c. Integer: $-5,0,\sqrt{4}$
d. Rational: $-5,-0.\overline{3},0, \sqrt{4}$
e. Irrational: $\sqrt{2}$
f. Real: all of them
Work Step by Step
The set of natural numbers is { 1, 2, 3, 4, 5, ... } .
The set of whole numbers is { 0, 1, 2, 3, 4, 5, ... }
The set of integers is {... , -4, -3, -2, -1,0, 1, 2, 3, 4,...}
The set of rational numbers$: \displaystyle \frac{a}{b},\ b\neq 0$, and b integers
Irrational numbers: are not rational (can not be written as $\displaystyle \frac{a}{b},\ b\neq 0$)
Real numbers: all rational and irrational numbers.
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$-5$ is a negative integer, all integers are rational
$-0.\displaystyle \overline{3}=-\frac{1}{3}$ is a rational number
$0$ is a whole number, an integer, rational
$\sqrt{5 }$ is irrational
$\sqrt{4}=2,$ natural, whole, integer, rational.
a. Natural: $\sqrt{4}$
b. Whole: $0,\sqrt{4}$
c. Integer: $-5,0,\sqrt{4}$
d. Rational: $-5,-0.\overline{3},0, \sqrt{4}$
e. Irrational: $\sqrt{2}$
f. Real: all of them
