Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 28
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37MODULE -
1
Exponents and Radicals
Algebra
In other words, the process of converting surds to rational numbers is called rationalisation
and two numbers which on multiplication give the rational number is called the rationalisation
factor of the other.
Notes
3 +
3 −
For example, the rationalising factor of x is x , of
is
.
2
2
Note:
x −
x +
(i) The quantities
and
are called conjugate surds. Their sum and product
y
y
are always rational.
(ii) Rationalisation is usually done of the denominator of an expression involving irrational
surds.
Let us consider some examples.
Example 2.29:
Find the rationalising factors of 18 and
.
12
×
×
=
Solution:
18 =
3
3
2
3
2
∴ Rationalising factor is 2 .
×
×
=
=
.
12
2
2
3
2
3
∴ Rationalising factor is 3 .
+
2
5
Example 2.30:
Rationalise the denominator of
.
−
2
5
(
)(
)
(
)
2
+
+
+
+
2
5
2
5
2
5
2
5
=
(
)(
)
Solution:
=
−
−
−
+
3
2
5
2
5
2
5
+
7
2
10
7
2
=
−
=
−
−
10
3
3
3
+
4
3
5
Example 2.31:
Rationalise the denominator of
.
−
4
3
5
(
)(
)
+
+
+
4
3
5
4
3
5
4
3
5
(
)(
)
Solution:
=
−
+
−
4
3
5
4
3
5
4
3
5
+
+
16
45
24
5
61
24
=
−
−
5
=
−
16
45
29
29
66
Mathematics Secondary Course
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