Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 25
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37MODULE -
1
Exponents and Radicals
Algebra
2.14.2 Multiplication and Division in Surds
Two surds can be multiplied or divided if they are of the same order. We have read that the
order of a surd can be changed by multiplying or dividing the index of the surd and index
Notes
of the radicand by the same positive number. Before multiplying or dividing, we change
them to the surds of the same order.
Let us take some examples:
[
]
×
=
×
=
3
2
3
2
6
3
and
2
are
of
same
order
12
÷
=
=
12
2
6
2
Let us multiply 3 and
3
2
=
=
6
3
6
3
3
27
2 =
3
6
4
∴
×
=
×
=
3
6
6
6
3
2
27
4
108
6
3
27
27
=
=
6
and
3
6
4
2
4
Let us consider an example:
Example
2.25:(i) Multiply
and
.
3
3
5
16
11
40
(ii) Divide
by
.
3
6
15
13
6
5
Solution:
(i)
×
3
3
5
16
11
40
×
×
×
×
×
×
×
×
×
=
3
3
5
11
2
2
2
2
2
2
2
5
×
×
=
3
3
55
2
2
2
5
=
3
220
10
6
2
3
15
13
5
13
5
169
=
=
.
(ii)
6
6
6
2
2
5
6
5
5
Example 2.26:
Simplify and express the result in simplest form:
×
×
2
50
32
2
72
Mathematics Secondary Course
63
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