NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

# NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 are the part of NCERT Solutions for Class 9 Maths. In this post, you will find the NCERT Solutions for Class 9 Maths Chapter 1 Number System Ex 1.2.

## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

Ex 1.2 Class 9 Maths 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 √m, where m is a natural number.
(iii) Every real number is an irrational number.

Solution:
(i) True
Because the collection of all rational numbers and all irrational numbers is called a set of real numbers.
(ii) False
Because negative numbers cannot be the square root of any natural number.
(iii) False
Because real numbers have rational and irrational both types of numbers. For example, 5, ½, 12, 2/3, etc. are real numbers but they are not irrational.

Ex 1.2 Class 9 Maths 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.

Solution:
No, if we take a positive integer, say 16, its square root is 4, which is a rational number. Again, the square root of 25 is 5 which is a rational number.

Ex 1.2 Class 9 Maths Question 3.
Show how √5 can be represented on the number line.

Solution:
Method 1:

Draw a number line and mark a point O on it. Take a point A on it such that OA = 1 unit. Draw BA OA as BA = 1 unit. Join OB = √2 units.
Now draw BB1
OB such that BB1 =1 unit. Join OB1 = √3 units.
Next, draw B1B2
OB1 such that B1B2 = 1 unit. Join OB2 = √4 = 2 units.
Again, draw B2B3
OB2 such that B2B3 = 1 unit. Join OB3 = √5 units.

Take O as centre and OB3 as radius, draw an arc which cuts the number line at D. Point D represents √5 on the number line and OD = √5 units.

Method 2: We have √5 = √(4 + 1) = √(22 + 12)

Draw a number line and mark a point O on it. Mark … , -2, -1, 0, 1, 2, … as shown in the figure below. Take a point Q such that OQ = 2 units. Draw PQ OQ. With point Q as centre and radius as 1 unit, cut an arc at P. Join OP.

Now, O as centre and OP as radius, draw an arc which cuts the number line at R. Point R represents √5 and OR = √5.

We can verify the result using Pythagoras theorem,

OP2 = OQ2 + PQ2

OP2 = 22 + 12

OP2 = 4 + 1

OP2 = 5

OP = √5

OR = OP = √5 units

Ex 1.2 Class 9 Maths Question 4.

A classroom activity (constructing the ‘square root spiral’).

Solution:
Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP, of unit length (see figure).

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, …