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.

Solution –

(i) True

Reason: Real number is a collection of both rational numbers and irrational numbers. So, every irrational number is a real number.

For example, √2 is an irrational number which is a real number.

(ii) False

Reason: A number line may have positive or negative number and no negative can be a square root of any natural number.

For example, √1/2 is a real number on the number line but 2/3 is not a natural number.

(iii) False

Reason: Real number is a collection of both rational numbers and irrational numbers.

For example, 4/5 is a rational number which is a real number but it is not an irrational number.

Related Questions –

• Are the square root of all positive integers irrational If not give an example of the square root of a number that is a rational number
• Show how root 5 can be represented on the number line