Squares, Cubes & Roots (WJEC GCSE Maths & Numeracy (Double Award)): 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

• 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:

    •