INDICES AND POWER NOTATION
When a number is multiplied by itself repeated times, we can re-write with
indices notation.
Example
2 × 2 × 2 × 2 × 2 can be written as 25. We read 25 as 2 power 5.
25 = 32
SQUARE NUMBERS , CUBE NUMBERS, SQUARE ROOTS AND CUBE
ROOTS
Lesson Objectives
Review squares and square roots.
Review cubes and cube roots.
Evaluate squares and square roots involving fractions.
SQUARE NUMBERS
Numbers with indices power 2 is spoken as “number squared”, example 5 2 is
verbally spoken as five squared. The answer to number squared are square
numbers. i.e. 52 = 25. As such 25 is part of the square number family.
Numbers with power 2
SQUARE
NUMBERS
12 = 1×1= 1
22 = 2×2= 4
32 = 3×3= 9
42 = 4×4= 16
52 = 5×5= 25
62 = 6×6= 36
72 = 7×7= 49
82 = 8×8= 64
92 = 9×9= 81
102 = 10 × 10 = 100
112 = 11 × 11 = 121
122 = 12 × 12 = 144
1
2
CUBE NUMBERS
Numbers with indices power 3 is spoken as “number cubed”, example 4 3 is
verbally spoken as four cubed. The answer to number cubed are cube numbers.
i.e. 43 = 64. As such 64 is part of the cube number family.
Numbers with power 3
CUBE
NUMBERS
13 = 1×1×1= 1
23 = 2×2×2= 8
33 = 3×3×3= 27
43 = 4×4×4= 64
53 = 5×5×5= 125
63 6×6×6= 216
Square root and Cube root is the reverse to square and cube root. The symbol for square root
is √ ❑ and the symbol for cube root is √ ❑.
3
For big numbers, we can evaluate without For mixed numbers, we must express the
calculators by expressing the numbers in numbers in improper fraction first before
the form of its factors. evaluating its square root or cube root.
Example. Evaluate the square root of 6400. 17
Example. Evaluate the cube root of 4
Solution: √ 64 ×100 27
= √ 64 × √ 100
= 8 × 10
Solution
√
3
4
17
27
= 80
=
5
3
√ 125
27
=
3
2
=1
3
3
Example: Evaluate the following
(1) 72 (2) 43 (3) √ 64
(4) √
3
64 . (5) √ 900 (4) √
3
8000.
Fractions need to be in improper fraction before evaluating squares and square roots
Example: Evaluate the following
( 23 )
(1) 1 2
( 14 )
(2) 2 2
(3)
(√ 1 1125 ) (4)
(√ 7 19 )
4
NAME: _______________________________________ CLASS: ___________
Exercise
1) Between 1 and 100, circle the square numbers.
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 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
2) List the cube numbers between 1 to 200. (You may use calculator to evaluate
the values).
……………………………………………………………………………………………………..
3) Evaluate the following. 5) Change the following fractions into
1 52 improper fraction hence evaluate.
2
3
33
√ 144
a. 2
4( )
3 2
√ 64
( )
2
4 2
b. 1
5 √3 216 5
6 √3 64
c. 3
√6
25
4) Without the use of calculator,
evaluate the following,
a) √ 6400
d. 6
√
1
4
b) √ 8100 6) Evaluate without the use of
c) √3 64000 calculator:
d) √3 27000 a. 4 2 +9
b. 13 +33
c. (4+3)2
d. 22 + 23
e. 52−7
f. √3 9 ×3
5
6
