Question

1. State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form Vm, where m is a natural number.
(iii) Every real number is an irrational number.​

Answer 1

(i) True

Reason: Real numbers are any number which can we think about. Thus, every irrational number is a real number.

(ii) False

Reason: A number line may have negative or positive number. Since, no negative can be the square root of a natural number, thus every point on the number line cannot be in the form of √m, where m is a natural number.

(iii) False

Reason: All numbers are real number and non terminating numbers are irrational number. For example 2, 3, 4, etc. are some example of real numbers and these are not irrational.