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Types of Number- GCSE Edexcel

Square roots and cube roots

√ is the square root sign. Taking the square root is the opposite of squaring.

For example, √25 = + or - 5 since 5² = 25 (-5)² = 25.

3√ is the cube root sign. Taking the cube is the opposite of cubing.

For example, 3√8 = 2 since 2^3 = 8

Squares and Cubes

Square numbers

Any number raised to the power 2 gives a square number. For example, 6² = 6x6 =36 (six squared)

There are LOTS of square numbers such as:

1x1= 1, 2x2=4, 3x3=9, 4x4=16, 5x5=25, 6x6=36, 7x7=49, 8x8=64, 9x9=81, 10x10=100, 11x11=121, 12x12=144, 13x13=169, 14x14=196, 15x15=225

For the exams it would help if you knew up to 15²

Cube Numbers

Cube numbers are when a number is raised to the power of 3. For example, 2^3= 2x2x2= 8 (two cubed)

Like square numbers, there are a lot of cubed numbers such as:

1x1x1=1, 2x2x2=8, 3x3x3=27, 4x4x4=64, 5x5x5=125, 6x6x6=216 etc...

Cube and square numbers will often appear in number sequence questions.

Multiples

Multiples are the numbers that are in multiplication tables. For example 3,6,9,12,15,18 are all multiples of 3.

Reciprocals

The reciprocal of a number a/x is x/a (=x÷a). Multiplying a number by its reciprocal always gives 1. Zero has no reciprocal.

Examples

The reciprocal of 2/3 is 3/2

The reciprocal of 4 is 1/4 (4 is the same as 4/1)

To find the reciprocal of 1 2/3, first put it in the form a/x (12/3=5/3), then invert it (3/5)

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