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NCERT solution class 9 chapter 1 Number Systems exercise 1.2 mathematics

EXERCISE 1.2


Page No 8:

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, where m is a natural number.

(iii) Every real number is an irrational number.

Answer:

(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 number.

(iii) False; as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number.

 


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.

Answer:

If numbers such asare considered,

Then here, 2 and 3 are rational numbers. Thus, the square roots of all positive integers are not irrational.

 


Question 3:

Show howcan be represented on the number line.

Answer:

We know that,

And, 

Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length perpendicular to OA. Then, taking O as centre and OB as radius, draw

an arc intersecting number line at C.

C is representing.

 


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