Detailed solution to all exercise questions of NCERT book for CBSE Class 9 Math in Chapter 1 - Number Systems - exercise 1.2. The exercise comprises 4 questions. Solution to 2 of the 4 questions provided in this webpage.
Key concepts covered in this exercise include properties of rational numbers, irrational numbers, and real numbers.
State whether the following statements are true or false and justify:
(i) Every irrational number is a real number.
TRUE. Real numbers are made up of rational numbers and irrational numbers. Therefore, every irrational number is a real number. Eg. √2 is an irrational number which is also a real number.
ii) Every point on the number line is of the form √m , where m is a natural number.
FALSE. m could be 0 or an irrational number. Eg. √(0 ) = 0 which is not a natural number.
iii) Every real number is an irrational number.
FALSE. Real numbers are made up of rational numbers and irrational numbers. Rational numbers are not irrational numbers. So, not all real numbers are irrational numbers.
Eg. 43 is a real number but is not an irrational number.
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.
NO. No, not all the square roots of positive integers are irrational. Eg. √4 = 2 which is not an irrational number.