EXPONENTS SQUARE AND CUBED NUMBERS

TYPES OF NUMBERS

•Identify the set of:
a) Prime and Composite Numbers
b) Square, Cube and Triangular numbers.

Number Theory Unit Objectives

PRIME NUMBERS

•DEFINITION: A prime number can be divided,
without a remainder, only by itself and by 1. For
example, 17 can be divided only by 17 and by 1.

Exa

mples: 2, 3, 5, 7, 11, 13, 17, 19

COMPOSITE NUMBER

• Definition: A whole number that can be divided

evenly by numbers other than 1 or itself.

• Example: 9 can be divided evenly by 3 (as well as 1

and 9), so 9 is a composite number.

SQUARE NUMBER

• Also called a “perfect square”

• A whole number multiplied by itself creates a square

number.

• It can be represented by arranging objects in a square.

SQUARE NUMBER?

The product of a number multiplied by itself.

2

×

2

3

×

3

4

×

4

4

9

16

SQUARE NUMBERS

• 1 x 1 = 1

• 2 x 2 = 4

• 3 x 3 = 9

• 4 x 4 = 16

•5 x 5 = 25

•6 x 6 = 36

•7 x 7 = 49

•8 x 8 = 64

 9 x 9 = 81

 10 x 10 = 100

 11 x 11 = 121

 12 x 12 = 144

13 x 13 = 169

14 x 14 = 196

15 x 15 = 225

A square root is the opposite of squaring a number.

32 = 9

So… 9 = 3

A square root of a number is a value that can
be multiplied by itself to give the original
number!

A square root of 9 is 3, because when 3 is multiplied
by itself you get 9!

Square

3 9

Square
Root

SQUARE ROOTS

Example:

has two answers:

+7 is called the positive or principal
square root.
-7 is called the negative square root.

49

SQUARE ROOTS

Example:

because

Also

because

7

49 =

7

49

−=

7 × 7 = 49

−7 × −7 = 49

2

2

2

2 x 2 x 2 = 8

CUBE NUMBERS

▪A Cube Number is the result when a
number is raised to the third power.

𝟐𝟑= 2 x 2 x 2 = 8

The opposite of cubing a number is finding the cube root.
Since 53= 125, the cube root of 125 is 5. The cube root
of a perfect cube is an integer.

CUBE NUMBERS

• Here are the first few cube numbers:

1 (=1×1×1)
8 (=2×2×2)
27 (=3×3×3)
64 (=4×4×4)
125 (=5×5×5)

CUBE ROOTS

▪The Cube Root of a number
tells which number was
originally raised to the third
power.

𝟑 𝟖 = 2

A cube root goes the in the opposite direction of having something cubed

𝟑𝟑= 𝟐𝟕
𝟑 𝟐𝟕 = 𝟑

▪The cube root of a number is a special value that when cubed gives

the original number!

▪The cube root of 27 is 3, because when 3 is cubed you get 27!

cube

3 27

cube
root

25

•

Counting number

•

Whole number

•

Integer

•

Square Number

•

Multiple of

5

and

25

•

Factor of

50

and

100

WHAT

TYPE OF
NUMBER

IS 25?

A number that can make a triangular dot pattern.

Example: 1, 3, 6, 10 and 15 are triangular numbers.

Triangular Numbers