Chapter 2. Exponents and Radicals

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