Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 31
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37MODULE -
1
Exponents and Radicals
Algebra
•
Operations on surds
1
1
1
1
⎛
⎞
n
⎛
⎞
⎛
⎞
x
x
n
1
1
1
1
1
m
n
=
⎜ ⎜
⎟ ⎟
1
( )
⎜
⎟
⎜
⎟
×
=
=
=
x
n
y
n
xy
;
x
n
x
mn
x
m
;
⎜
⎟
⎜
⎟
n
1
Notes
⎝
y
⎠
⎝
⎠
⎝
⎠
n
y
( )
m
( )
a
an
( )
1
1
1
;
=
=
=
=
=
m
m
a
mn
an
a
an
x
x
n
x
x
or
x
x
m
x
mn
x
n
m
mn
•
Surds are similar if they have the same irrational factor.
•
Similar surds can be added and subtracted.
•
Orders of surds can be changed by multiplying index of the surds and index of the
radicand by the same positive number.
•
Surds of the same order are multiplied and divided.
•
To compare surds, we change surds to surds of the same order. Then they are compared
by their radicands alongwith co-efficients.
•
If the product of two surds is rational, each is called the rationalising factor of the
other.
•
x +
x −
is called rationalising factor of
and vice-versa.
y
y
TERMINAL EXERCISE
1. Express the following in exponential form:
(i) 5 × 3 × 5 × 3 × 7 × 7 × 7 × 9 × 9
⎛ −
⎛ −
⎛ −
⎛ −
⎞
⎞
⎞
⎞
7
7
7
7
× ⎟
× ⎟
× ⎟
⎜
⎜
⎜
⎜
⎟
(ii)
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
9
9
9
9
2. Simplify the following:
3
2
3
⎛
⎞
⎛
⎞
⎛
⎞
5
7
3
−
×
×
⎜
⎟
⎜
⎟
⎜
⎟
(i)
⎝
⎠
⎝
⎠
⎝
⎠
6
5
7
2
2
⎛
⎞
⎛
⎞
3
35
1
×
×
−
⎜
⎟
⎜
⎟
(ii)
⎝
⎠
⎝
⎠
7
27
5
3. Simplify and express the result in exponential form:
( ) ( ) ( )
×
×
2
2
2
(i)
10
6
5
Mathematics Secondary Course
69
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education