Class-9 Subject-Maths Chapter-1 Exercise1.2 (NUMBER SYSTEM)

 

EVENTS CONVENT HIGH SCHOOL
05/08/2021          CLASS-9         SESSION2021-22(SLOT-1)
Maths
Chapter-1 EXERCISE 1.2
NUMBER SYSTEM
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 Question 1.State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.
(i) True-Because all rational numbers and all irrational numbers form the group (collection) of real numbers.

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

(ii) False-Because negative numbers cannot be the square root of any natural number.

 (iii) Every real number is an irrational number.

 (iii) False-Because rational numbers are also a part of real numbers.

 

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:No, if we take a positive integer, say 9, its square root is 3, which is a rational number.

 

Question 3.Show how √5 can be represented on the number line.

Solution:Draw a number line and take point O and A on it such that OA = 1 unit. Draw BA ⊥ OA as BA = 1 unit. Join OB = √2 units.

Now draw BB1 ⊥ OB such that BB1 =1 unit. Join OB1 = √3 units.

Next, draw B1B2⊥ OB1such that B1B2 = 1 unit.

Join OB2 = units.

Again draw B2B3 ⊥OB2 such that B2B3 = 1 unit.

Join OB3 = √5 units.

Take O as centre and OB3 as radius, draw an arc which cuts the number line at D.

Point D

represents √5 on the number line.