Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 21
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37MODULE -
1
Exponents and Radicals
Algebra
1
⎛
⎞
1
1
1
3
3
⎜
⎟
=
=
=
=
=
×
=
3 2
6
2
3
2 3
6
7
7
2
7
2
7
7
7
7
(iii)
⎜
⎟
⎝
⎠
Notes
( )
3
9
1
×
(iv)
×
=
=
=
=
=
5
3
3
15
9
3
5
3
3
5
15
4
4
4
4
4
4
5
Thus, we see that the above laws of surds are verified.
An important point: The order of a surd can be changed by multiplying the index of the
surd and index of the radicand by the same positive number.
For example
=
=
6
2
3
6
2
2
4
=
=
and
8
2
4
8
3
3
9
2.12 SIMILAR (OR LIKE) SURDS
Two surds are said to be similar, if they can be reduced to the same irrational factor,
without consideration for co-efficient.
75 =
For example,
and
are similar surds. Again consider
and
3
5
7
5
5
3
12 =
. Now
75 and
are expressed as
. Thus, they are
2
3
5
3
and
2
3
12
similar surds.
2.13 SIMPLEST (LOWEST) FORM OF A SURD
A surd is said to be in its simplest form, if it has
a) smallest possible index of the sign
b) no fraction under radical sign
n
c) no factor of the form a
, where a is a positive integer, under the radical sign of index n.
×
125
125
12
5
=
=
3
12
For example,
3
3
×
18
18
12
6
Let us take some examples.
Example 2.20:
Express each of the following as pure surd in the simplest form:
3
32
(i)
(ii)
(iii)
4
2
7
4
7
4
Mathematics Secondary Course
59
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