Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 17
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37MODULE -
1
Exponents and Radicals
Algebra
A surd is defined as a positive irrational number of the type
x , where it is not possible to
n
find exactly the nth root of x, where x is a positive rational number.
The number
x is a surd if and only if
n
Notes
(i) it is an irrational number
(ii) it is a root of the positive rational number
2.7.1 Some Terminology
In the surd
x , the symbol
is called a radical sign. The index ‘n’ is called the order
n
of the surd and x is called the radicand.
Note:
i)
When order of the surd is not mentioned, it is taken as 2. For example, order
(
)
7 =
of
2
is 2.
7
ii)
8 is not a surd as its value can be determined as 2 which is a rational.
3
iii)
2 +
, although an irrational number, is not a surd because it is the square
2
root of an irrational number.
2.8 PURE AND MIXED SURD
i) A surd, with rational factor is 1 only, other factor being rrational is called a pure surd.
For example,
16 and
50 are pure surds.
5
3
ii) A surd, having rational factor other than 1 alongwith the irrational factor, is called a
mixed surd.
For example,
are mixed surds.
3
2
3
and
3
7
2.9 ORDER OF A SURD
In the surd
, 5 is called the co-efficient of the surd, 3 is the order of the surd and 4
3
5
4
is the radicand. Let us consider some examples:
Example 2.16:
State which of the following are surds?
3
3
(i)
49
(ii)
96
(iii)
81
(iv)
256
Mathematics Secondary Course
55
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