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.

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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.

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Similar questions

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.

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.

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