Basic, GCSE(F),

A **Square Number** is the result of multiplying an integer by itself. For example, 4 x 4 = 16. The first 5 square numbers are shown below in a diagram form:

A shorthand way of writing a square number is to use an **index**: 4 x 4 = 4^{2}.

Square numbers can be written as a sequence:

Term | 1 | 2 | 3 | 4 | 5 | ... |
---|---|---|---|---|---|---|

1^{2} | 2^{2} | 3^{2} | 4^{2} | 5^{2} | ... | |

Value | 1 | 4 | 9 | 16 | 25 | ... |

1. What is the next square number after 81?

Answer: 100

81 is 9^{2}. The next square number is 10^{2}, which is 100.

2. What is the value of the 12^{th} square number?

Answer: 144

12 x 12 = 144.

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