Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 18
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37MODULE -
1
Exponents and Radicals
Algebra
Solution:
(i)
49 = 7, which is a rational number.
∴ 49 is not a surd.
Notes
=
×
×
=
(ii)
96
4
4
6
4
6
∴ 96 is an irrational number.
⇒ 96 is a surd.
=
×
×
×
=
(iii)
, which is irrational
3
3
3
81
3
3
3
3
3
3
∴
81 is a surd.
3
=
×
×
×
=
(iv)
3
3
3
256
4
4
4
4
4
4
∴
256 is irrational.
3
⇒
256 is a surd
3
∴ (ii), (iii) and (iv) are surds.
Example 2.17:
Find “index” and “radicand” in each of the following:
5
4
4
(i)
117
(ii)
162
(iii)
213
(iv)
214
Solution:
(i)
index is 5 and radicand is 117.
(ii)
index is 2 and radicand is 162.
(iii)
index is 4 and radicand is 213.
(iv)
index is 4 and radicand is 214.
Example 2.18:
Identify “pure” and “mixed” surds from the following:
(i) 42
(ii)
(iii)
3
4
4
18
2
98
Solution:
(i) 42 is a pure surd.
(ii)
is a mixed surd.
3
4
18
(iii)
is a mixed surd.
4
2
98
2.10 LAWS OF RADICALS
Given below are Laws of Radicals: (without proof):
[ ]
n
=
(i)
n
a
a
56
Mathematics Secondary Course
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