State whether the following statements are true or false. Justify your answer.

(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.

Open in App

Solution

(i) True.
Since the collection of real numbers is made up of rational and irrational numbers.
For example,
$\sqrt{2}$ is a real number.

(ii) The given statement is false.
All negative numbers cannot be expressed as the square root of any other number.

Suggest Corrections

Similar questions

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.

Question 1 (ii)
State whether the following statement is true or false. Justify your answer.

Every point on the number line is of the form $\sqrt{m}$ , where m is a natural number.

Question 1 (i)
State whether the following statement is true or false. Justify your answer.

Every irrational number is a real number.

Question 1 (iii)
State whether the following statement is true or false. Justify your answer.

Every real number is an irrational number.

Every point on the number line is of the form $\sqrt{m},$ where m is a natural number. State true or false

Join BYJU'S Learning Program