Tuesday, July 27, 2010

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, where m is a natural number.
(iii) Every real number is an irrational number.
Ans.
(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.

Ans. 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.

Ans.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.