9999 Squared In Your Head! - video powered by Metacafe
This is a great approach to squaring large numbers mentally. Once you understand the concept of a reference number (referred to as a base number in the video), it's not hard to do mentally. You can practice with numbers up to 125 over at mathpath, too.
If you would like to learn to go the other direction, over at the Grey Matters Mental Gym, I can teach you how to extract cube roots, square roots and even fifth roots!
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