Exercise - 1.2

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.

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