Exercise 1.2

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

(i) Every irrational number is a real number : TrueFalse.

Since irrational numbers fall within the category of real numbers, every irrational number is indeed a real number.

(ii) Every point on the number line is of the form where m is a natural number : FalseTrue.

The number line includes all real numbers, which means it contains not just natural numbers but also integers,rational numbers,and irrational numbers.

(iii) Every real number is an irrational number : FalseTrue.

Since there are real numbers not every real number is irrational.

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number. NoYes

Example: Take positive integer 4 : 4 = .

Then, we know that 2 is a rationalirrational number.

Thus, not all the square roots of positive integers are irrational.

Show how 5 can be represented on the number line.

We know that 5 = 4+1 = 22+12. Thus, we draw a perpendicular of length unit at number on the numberline.

Now, join the hypotenuse i.e. joining "0"(zero) and point O.

Projecting it onto the numberline, we get 5.

We see that point B denotes 5 on the numberline.