Question

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 $\sqrt{m}$, where $m$ is a natural number.
(iii) Every real number is an irrational number.

Answer 1

(i) True: Real numbers are any number which can we think.

Thus, every irrational number is a real number.

(ii) False: A number line may have negative or positive number.

Since, no negative can be the square root of a natural number, thus every point the the number line cannot be in the form of $\sqrt{m}$, where $m$ is a natural number.

(iii) False: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.