Question-1 :- 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; since the collection of real numbers is made up of rational and irrational numbers.
(ii) False; as negative numbers cannot be expressed as the square root of any other no.
e.g. √-4, √-9 etc.
(iii) False; as real numbers include both rational and irrational numbers.
Therefore, every real no. cannot be an irrational no.
Question-2 :- 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.
Solution :- If numbers such as √36=6 and √49=7 are considered,
Then here, 6 and 7 are rational numbers. Thus, the square roots of all positive integers are not irrational.
Question-3 :- Show how √5 can be represented on the number line.
Solution :-Using Pythagoras theorem that OB=√ 1²+4² =√5 By using the compass, with centre O and radius OB, draw an arc which intersecting the number line at the point P. Then P corresponds to √5 on the number line.
