Ex 1.2

                                              Maths NCERT Book Solutions

                                                                  Chapter 1

                                                                   Ex.1.2

Q: 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 real numbers consists of rational and irrational numbers. (ii)  False, Since negative integers cannot be expressed as the  square root of any natural number. (iii)  False, real number includes both rational and irrational numbers. So every real number can not be an irrational number. Concept Insight: Mentioning the reasons is important in this problem. Real Numbers consists of rational and irrational numbers and not vice versa. Every real number corresponds to a point on number line and vice versa. Recall real number includes negative numbers also. Square root of negative numbers is not defined. Q: 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 Square roots of all square numbers is rational.   For example       Thus the square roots of all positive integers are not irrational Concept Insight: In general only the square root of a prime number is irrational. There are the perfect square numbers.  Q: 3 Show how  can be represented on the number line.   Answer Using Pythagoras Theorem: 5=22+12 Taking positive square root we get        1.  Mark a point 'A' representing 2 units on number line. 2. Now construct AB of unit length perpendicular to OA. Join OB 3. Now taking O as centre and OB as radius draw an arc, intersecting number line at point C. 4. Point C represents   on number line Concept Insight: For a positive integer n,   can be   located on number line ,  if    is located using Pythagoras Theorem . If   is a perfect square then this method is useful.    To represent the irrational number   key idea is to use Pythagoras theorem and create a length of   units by constructing a right triangle of base and perpendicular  of length 2 and 1 units.