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.

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Solution

(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.

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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.

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

Every real number is an irrational number.

Find whether the following statements are true or false :

(i) Every real number is either rational or irrational.

(ii) $π$ is an irrational number.

(iii) Irrational numbers cannot be represented by points on the number line.

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

Every irrational number is a real 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.

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