Squares, Cubes & Roots (Cambridge (CIE) IGCSE Maths): Revision Note
Squares, Cubes & Roots
What are square numbers?
A square number is the result of multiplying a number by itself
The first square number is
, the second is
and so on
The first 15 square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Aim to remember at least the first fifteen square numbers
In algebra, square numbers can be written using a power of 2
What are cube numbers?
A cube number is the result of multiplying a number by itself, twice
The first cube number is
, the second is
and so on
The first 5 cube numbers are 1, 8, 27, 64 and 125
Aim to remember at least the first five cube numbers
You should also remember 103 = 1000
In algebra, cube numbers can be written using a power of 3
What are square roots?
The square root of a value, is the number that when multiplied by itself equals that value
For example, 4 is the square root of 16
It is the opposite of squaring
Square roots are indicated by the symbol
e.g. The square root of 49 would be written as
Square roots can be positive and negative
e.g. The square roots of 25 are 5 and -5
If a negative square root is required then a - sign would be used
e.g.
but
Sometimes both positive and negative square roots are of interest and would be indicated by
The square root of a non-square integer is also called a surd
e.g.
is a surd, as 3 is not a square number
surds are irrational numbers
where possible modern calculators will display irrational numbers as surds
is rational, as it is equal to 8
64 is a square number
However,
is irrational
2 is not a square number
You should aim to remember the square roots of the first 15 square numbers:
What are cube roots?
The cube root of a value, is the number that when multiplied by itself twice equals that value
For example, 3 is the cube root of 27
It is the opposite of cubing
Cube roots are indicated by the symbol
e.g. The cube root of 64 would be written as
You should remember the values of the following cube roots:
Worked Example
Write down a number which is both a cube number and a square number, and hence express this number in two different ways using powers of 2 and 3.
Listing the first 12 square numbers
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Listing the first 5 cube numbers
1, 8, 27, 64, 125
64 appears in both lists, it is the 8th square number and 4th cube number
64 is both a square and cube number
64 = 82 and 64 =43
You've read 0 of your 5 free revision notes this week
Sign up now. It’s free!
Did this page help you?