These NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Exercise 1.2
State whether the following statements are true or false. Justify your answer.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form √m where m is a natural number.
(iii) Every real number is an irrational number.
(i) True, because the set of every rational and every irrational number is called real number.
(ii) False, no negative number can be the square root of any natural number.
(iii) False, because a real number is the set of every irrational and rationed number. For example, 2 is real but not irrational.
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, the square roots of all positive integers are not always irrational.
For e.g. 4 is a positive integer and the value of their square root is 2. Which is a rational number.
Show how √5 can be represented on the number line.
To represent √5 on the number line, taking O at zero on the number line.
Again taking OA = 2 unit in the positive direction of the number line.
Again draw BA ⊥ OA and the length of BA = 1 unit.
Join BO and complete a right-angle ∆OAB.
Now, the length of BO = √5 (by Pythagoras theorem).
Again we take OB as a radius and draw a circle which cuts the number line at C.
Therefore, the length of OC is also equal to √5.
Hence point C is the required point on the number line.
Classroom activity (Constructing the ‘square root spiral’).
Take a large sheet of paper and construct the ‘square spiral’ in the following fashion. Start with a point O and draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.2). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn-1Pn by drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3…, Pn…, and joined them to create a beautiful spiral depicting √2, √3, √4……
Fig. Constructing square root spiral.