# Squares of Numbers That End in 5

A number that ends in 5 has the form

Why does this work?

A² | = (10a + 5)² | |

= 100a² + 2·10a·5 + 25 | ||

= 100a(a + 1) + 25. |

Which exactly means that 25 is appended to the product

Another example: to compute 245² observe that a = 24. Then

24·(24 + 1) = 24² + 24 = 576 + 24 = 600.

Therefore 245²=60025. Here is another way to compute 24·25:

24·25 = 2400/4 = 1200/2 = 600.

The rule naturally applies to 2-digit numbers as well.

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