# Squaring 2-Digit Numbers

Let's see an example different from the ones at the index page. Say, find 32².

First add the last digit (2) to the number itself: 32 + 2 = 34. Multiply the sum by the first digit:

Why does this work?

Let the number be N = 10a + b.

(10a + b)² | = 100a² + 20ab + b² |

= 10a(10a + 2b) + b² | |

= 10a(10a + b + b) + b² | |

= 10a(N + b) + b². |

So, to compute the square of N = 10a + b, first find N + b. Then multiply that by the first digit a to get

In fact the method is not restricted to 2-digit numbers. a may have 2 or more digits as well. The calculations become more complex of course.

Find 215². 215 + 5 = 220.

|Contact| |Front page| |Contents| |Algebra| |Math magic|

Copyright © 1996-2018 Alexander Bogomolny

65106238 |