Class 9 NCERT Mathematics Solutions
Exercise 1.2
All questions and answers
Q.1. State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
Ans. True, every irrational number is a real number because real numbers include both rational and irrational numbers.
Rational numbers:- A number is rational which can be written in the form of p/q, where p and q are integers and q≠0.
i.e. 7/2, 0.086, 0.23
Irrational numbers:- A number is irrational which cannot be written in the form of p/q, where p and q are integers and q≠0.
i.e. √2, √3, √5, √11, √13, √17, π ……
(ii) Every point on the number line is of the form √m, where m is a natural number.
Ans. False, because no negative number can be the square root of a natural number and on the number line, negative numbers are also expressed. So, the statement every point on the number line is of the form √m, where m is a natural number, is false.
(iii) Every real number is an irrational number.
Ans. False, because real numbers include both rational and irrational numbers. Thus every irrational number is a real number but every real number is not an irrational number.
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.
Ans. No, the square roots of all positive integers are not irrational.
Examples:- √16=4 (4 is a rational number)
√4=2 (2 is a rational number)
Q.3. Show how √5 can be represented on the number line.
Ans.
