Irrational numbers : A number which when expressed as a decimal that is
non-terminating or non-recurring (non-repeating) is called an irrational
number. Irrational numbers are denoted by ‘Q’, with a bar at the top. Irrational numbers cannot be
denoted in the form of p/q where p,q ϵ I and q≠0.
A square root of every non-perfect square is an irrational
number and similarly, cube roots of non-perfect cubes are also examples of
irrational numbers .
Examples of irrational numbers are
π =
3.141592…
= 1.414213…
How to locate irrational numbers on number line
Sqrt 2 on
the Number Line:
Let us construct the irrational numbers on number line shown
Take points A and B on the number line where A at 0 and B at 1. Therefore, AB = 1 unit.
Draw BC of unit length (1 unit) perpendicular to the number line (AB) Join AC
According to Pythagoras…triangle ABC,
Let us construct the irrational numbers on number line shown
Take points A and B on the number line where A at 0 and B at 1. Therefore, AB = 1 unit.
Draw BC of unit length (1 unit) perpendicular to the number line (AB) Join AC
According to Pythagoras…triangle ABC,
AC ^2=(AB^2 + BC^2)
AC =sqrt(1^2 + 1^2)
AC = sqrt 2 units.
With A as center and radius AC, draw an arc to cut the number line at P
on the right side and Q on the left side.
AP = sqrt 2 and AQ = -sqrt 2
units.
Therefore P and Q represent the point’s sqrt 2 and -sqrt 2 respectively on the number line
.
Therefore P and Q represent the point’s sqrt 2 and -sqrt 2 respectively on the number line
Sqrt 3 on the Number Line:
Represent sqrt 2 on the number line.
Draw PT of unit length perpendicular to the number line.
Joint AT.
triangle ATP
AT^2 =(AP^2 + TP^2)
AT =sqrt((2^2 + 1^2)
AT=sqrt(2 + 1)
With A as centre and radius AD draw an arc to cut the number line at R and S.
AR =sqrt3 and AS = -sqrt 3
R and S represent the point’s sqrt3 and -sqrt 3 respectively on the number line.
With A as centre and radius AD draw an arc to cut the number line at R and S.
AR =sqrt3 and AS = -sqrt 3
R and S represent the point’s sqrt3 and -sqrt 3 respectively on the number line.
sqrt 4.5
on the Number Line:
Take number line AB length with 4.5. extended 1 cm represent
as C
Take exactly mid point
at 2.75 represent as o. draw semi
circle cuts on number line.
Draw a line at 4.5
perpendicular to the number line which
cuts at semi circle ,represent as D.
The distance between BD is the sqrt of 4.5
Sqrt 10.5 in number
line :
Take number line AB length with 10.5. extended 1 cm
represent as C
Take exactly mid point
at 5.75 represent as o. draw semi
circle cuts on number line.
Draw a line at point
B perpendicular to the number line which
cuts at semi circle ,represent as D.
