- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.4
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5
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).
