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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(i) true. (ii) true. (iii) true.

(ii) false. (ii) false. (iii) true.

(i) true. (ii) false. (iii) false.

(i) true. (ii) false. (ii) true

answer is C.

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Detailed Solution

Concept- Real numbers are those numbers which can be shown on the number line. This includes natural, whole numbers, and integers. To solve the above problem we have to prove the following statements.
Here,
i). Real numbers are any number, even zero and negative numbers. Thus, every rational number is a real number. Therefore, this statement is true.
ii). Number lines have both negative and positive numbers. Hence, negative numbers can’t be square root of natural numbers. Thus, every point in the number line cannot be in form of

\sqrt{m} .

Therefore, this statement is false
iii). All numbers which are real numbers and also non terminating numbers are known as irrational numbers. Therefore, this statement is false.
Hence, the correct option is 3.

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