Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 2
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37MODULE -
1
Exponents and Radicals
Algebra
•
identify radicals from a given set of irrational numbers;
•
identify index and radicand of a surd;
•
state the laws of radicals (or surds);
Notes
•
express a given surd in simplest form;
•
classify similar and non-similar surds;
•
reduce surds of different orders to those of the same order;
•
perform the four fundamental operations on surds;
•
arrange the given surds in ascending/descending order of magnitude;
•
find a rationalising factor of a given surd;
1
1
and
•
rationalise the denominator of a given surd of the form
,
+
+
a
b
x
x
y
where x and y are natural numbers and a and b are integers;
•
simplify expressions involving surds.
EXPECTED BACKGROUND KNOWLEDGE
•
Prime numbers
•
Four fundamental operations on numbers
•
Rational numbers
•
Order relation in numbers.
2.1 EXPONENTIAL NOTATION
Consider the following products:
(i) 7 × 7
(ii) 3 × 3 × 3
(iii) 6 × 6 × 6 × 6 × 6
2
In (i), 7 is multiplied twice and hence 7 × 7 is written as 7
.
3
In (ii), 3 is multiplied three times and so 3 × 3 × 3 is written as 3
.
5.
In (iii), 6 is multiplied five times, so 6 × 6 × 6 × 6 × 6 is written as 6
2
7
is read as “7 raised to the power 2” or “second power of 7”. Here, 7 is called base and
2 is called exponent (or index)
3
Similarly, 3
is read as “3 raised to the power 3”or “third power of 3”. Here, 3 is called the
base and 3 is called exponent.
5
Similarly, 6
is read as “6 raised to the power 5”or “Fifth power of 6”. Again 6 is base and
5 is the exponent (or index).
40
Mathematics Secondary Course
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