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

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

m

, where

m

is a natural number.
(iii) Every real number is an irrational number.

Filo · Accepted Answer

(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

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.

Question Text	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 $m$ , where $m$ is a natural number. (iii) Every real number is an irrational number.
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

Practice questions from similar books

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 m​, where m is a natural number.(iii) Every real number is an irrational number.

Text solutionVerified

Practice questions from similar books

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