Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 16
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37MODULE -
1
Exponents and Radicals
Algebra
Solution:
1
( )
1
1
1
(
)
×
4
(i)
625 =
×
×
×
=
=
=
4
5 (
5
5
) 5
4
5
5
4
5
4
4
Notes
2
2
( )
2
×
(
)
2
5
(ii)
=
×
×
×
×
=
=
=
=
5
2
5
5
243
3 (
3
3
3
) 3
3
3
3
9
5
5
−
−
3
3
×
×
×
⎛
⎞
⎛
⎞
16
2
2
2
2
4
4
=
⎜
⎟
⎜
⎟
(iii)
×
×
×
⎝
⎠
⎝
⎠
81
3
3
3
3
−
3
⎛ −
⎞
3
⎡
⎤
×
−
⎜
⎟
4
4
3
3
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
4
2
2
2
3
27
⎝
⎠
4
=
=
=
=
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎢
⎥
=
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
⎢
3
⎥
3
3
2
8
⎣
⎦
CHECK YOUR PROGRESS 2.5
1. Simplify each of the following:
2
−
⎛
⎞
27
3
( )
3
⎜
⎟
(i)
(ii)
16
4
⎝
⎠
125
2. Simplify each of the following:
1
1
(
)
( )
−
−
÷
(i)
625
25
4
2
1
1
3
−
⎛
⎞
⎛
⎞
⎛
⎞
7
7
7
4
2
4
×
×
⎜
⎟
⎜
⎟
⎜
⎟
(ii)
⎝
⎠
⎝
⎠
⎝
⎠
8
8
8
3
1
3
−
⎛
⎞
⎛
⎞
⎛
⎞
13
13
13
4
4
2
×
×
⎜
⎟
⎜
⎟
⎜
⎟
(iii)
⎝
⎠
⎝
⎠
⎝
⎠
16
16
16
2.7 SURDS
We have read in first lesson that numbers of the type
are all irrational
, 2
3
and
5
numbers. We shall now study irrational numbers of a particular type called radicals or
surds.
54
Mathematics Secondary Course
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