1. The document discusses squares, square roots, cubes, and cube roots of numbers. It provides examples of evaluating expressions involving these concepts without and with a calculator. 2. Tables are included showing the first ten perfect squares and cubes. 3. Questions at the end provide practice evaluating additional expressions and problems involving squares, square roots, cubes and cube roots.

1. WAJA Mathematics PMR
SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
Skill A: Squares of Numbers
1. Write in expanded form,
(a) 42
= X (b) (1
4
1
)2
= X
2. Write the index form of
(a) 0.36 X 0.36 = (b) (- 2.5) X (- 2.5) =
3. Find the value of the following without using a scientific calculator.
(a) 52
= X =
(b) ( - 3)2
= X =
(c) 0.62
= X =
(d) [
4
3
]2
= X =
4. Estimate the value of the following.
(a) 7.82
≈ = =
(b) 30.12
≈ = =
(c) 1.042
≈ = =
(d) 0.0992
≈ = =
5. Use a scientific calculator to evaluate the following, correct to 3 decimal places where
necessary.
(a) 63.212
=
(b) 124.562
=
(c) - 1.01352
=
(d) ( 2
4
3
)2
=
6. Complete the table below to get the first ten perfect squares.
12
22
32
42
52
62
72
82
92
102
Skill B: Square Roots of Positive Numbers
Page 1 of 5
When a number is squared, the number is multiplied by itself.
The square root of a positive number
is the number when multiplying by
itself equals to the given number.
82
8 X 8

2. WAJA Mathematics PMR
1(a) Since 122
= 144. Thus 144 =
(b) Since 1.52
= 2.25. Thus 25.2 =
(c) Since (
4
3
)2
=
16
9
. Thus 





16
9
=
2. Evaluate each of the following without using a calculator.
(a) 25 = (b) 81 =
(c) 





81
49
= (d) 





25
11
1 =
3. Find the product of each of the following.
(a) 2 X 2 = =
(b) 5.2 X 5.2 =
(c) 002.0 X 002.0 =
(d)
7
4
2 X
7
4
2 =
(e) 2 X 8 = =
(f) 3 X 12 = =
4. Evaluate the following using a scientific calculator, correct to 3 decimal places.
(a) 90 =
(b) 1200 =
(c) 52.45 =
(d) 0345.0 =
(e)
12
7
4 =
5. Complete the table below.
1 4 9 16 25 36 49 64 81 100
Skill C: Cubes of Numbers
1.Complete the following.
(a) 53
= X X
Page 2 of 5
The cube of a number is the product of the
number multiplied by itself three times.
4
√

3. WAJA Mathematics PMR
(b) 1.33
= X X
(c) ( 2
5
1
) X ( 2
5
1
) X ( 2
5
1
) =
2. Find the value of the following without using a calculator.
(a) 43
= X X =
(b) 103
= X X =
(c) ( - 1)3
= X X =
(d) (
3
2
)3
= X X =
3. Estimate the value of the following.
(a) 2.33
≈ =
(b) 4.853
≈ =
(c) 1.233
≈ =
(d) (- 0.98)3
≈ =
4. Evaluate the following using a scientific calculator, correct to 3 decimal places.
(a) 12.33
=
(b) ( - 14.51)3
=
(c) 2.003493
=
(d) ( 3
7
2
)3
=
5. Complete the table below to get the first ten perfect cubes.
13
23
33
43
53
63
73
83
93
103
Skill D: Cube Roots of Numbers
1(a) Since 43
= 64. Thus 3
64 =
(b) Since 0.53
= 0.125. Thus 3
125.0 =
Page 3 of 5
The cube root of a number is the
number when multiplied by itself
twice, equals to the given number.
23

4. WAJA Mathematics PMR
(c) Since (
5
3
)3
=
125
27
. Thus 3
125
27






=
2. Evaluate each of the following without using a calculator.
(a) 3
8 =
(b) ( )3 64− =
(c) 3
027.0 =
(d) 3
64
27






=
(e) 3
125
1






=
3. Evaluate the following using a scientific calculator, correct to 4 decimal places.
(a) 3
60 =
(b) 3
1320 =
(c) 3
52.54 =
(d) 3
0945.0 =
(e) 3
12
7
2 =
4. Solve the following problems.
(a) 3
125 + 3
27 = + =
(b) 3
216 - 3
8 = - =
(c) 3
343 - 3
512 + 3
1000 = - + =
5.Complete the table below.
3
1 3
8 3
27 3
64 3
125 3
216 3
343 3
512 3
729 3
1000
Mastery Practice
1. Write in expanded form,
(a) 5.62
=
(b) 0.423
=
2. Write the index form of
(a) (- 1.34) X (- 1.34) =
Page 4 of 5

5. WAJA Mathematics PMR
(b) (
7
3
) X (
7
3
) X (
7
3
) =
3. Find the square root for each of the following.
(a) 8.2 X 8.2 =
(b) ( )123.0− X ( )123.0− =
4. Evaluate each of the following without using a calculator.
(a) 2 – 0.22
=
(b) - 27 + ( - 3)3
=
(c) 64 + 32
=
(d) 49 – 52
=
(e) 13
+ 3
125 - 22
=
(f) 22
34 + =
(g) 3
216 - ( - 4)2
=
(h) 3
64
27
+
16
1
=
5. Evaluate the following using a scientific calculator, correct to 3 decimal places.
(a) 10.12
– 2.33
=
(b) 3
167.12 + 56.3 =
(c) 2.452
- 67.34 + 3
89.54 =
(d) ( )3 78.0− + 564.0 - (- 0.23)2
=
(e) 3
756 ÷ 3.89 =
Page 5 of 5

6. WAJA Mathematics PMR
(b) (
7
3
) X (
7
3
) X (
7
3
) =
3. Find the square root for each of the following.
(a) 8.2 X 8.2 =
(b) ( )123.0− X ( )123.0− =
4. Evaluate each of the following without using a calculator.
(a) 2 – 0.22
=
(b) - 27 + ( - 3)3
=
(c) 64 + 32
=
(d) 49 – 52
=
(e) 13
+ 3
125 - 22
=
(f) 22
34 + =
(g) 3
216 - ( - 4)2
=
(h) 3
64
27
+
16
1
=
5. Evaluate the following using a scientific calculator, correct to 3 decimal places.
(a) 10.12
– 2.33
=
(b) 3
167.12 + 56.3 =
(c) 2.452
- 67.34 + 3
89.54 =
(d) ( )3 78.0− + 564.0 - (- 0.23)2
=
(e) 3
756 ÷ 3.89 =
Page 5 of 5