Squares, Cubes & Roots (Cambridge (CIE) IGCSE International Maths)

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

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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

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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:

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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:

    •