Answer
a. Natural number in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } is $\sqrt 4$.
b. Whole numbers in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are 0 and $\sqrt 4$.
c. In the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } the integers are 0, $\sqrt 4$ and -5.
d. In the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, -5, -0.3, 0, $\sqrt 4$ are rational numbers.
e. In the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, $\sqrt 2$ is only irrational number.
f. All the numbers in the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are real numbers.
Work Step by Step
a. Natural Numbers are the numbers used for counting. The only natural number in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } is $\sqrt 4$ because $\sqrt 4$ is 2.
b. Whole numbers consists of 0 with Natural numbers. So, the whole numbers in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are 0 and $\sqrt 4$.
c. The set of integers includes the negative of the natural numbers and the whole numbers. So in the set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } the integers are 0, $\sqrt 4$ and -5.
d. The set of rational numbers is the set of all numbers that can be expressed as a quotient of two integers, with the denominator not 0. Rational numbers can be expressed as terminating or repeating decimals. So,in the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, -5 (-5/1 = -5), -0.3 (-3/10 = -0.3), 0 (0=0/1), $\sqrt 4$ ($\sqrt 4$ =2= 2 /1) are rational numbers.
e. The set of irrational numbers is the set of all numbers whose decimal representations are neither terminating nor repeating and also cannot be expressed as a quotient of integers. In the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ }, $\sqrt 2$ is only irrational number.
f. Real Numbers are either rational or irrational. So all the numbers in the given set { -5, -0.3, 0,$\sqrt 2$, $\sqrt 4$ } are real numbers.
