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A trick to squaring numbers ending in 5 in seconds!

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Would you like to learn a trick to impress your friends with your immense mental arithmetic skills? Here’s a quick way to square any number ending in 5.

Take, for example, 75. What is 75^2?

  1. 5^2 = 25. So the answer ends in 25.
  2. 7 x 8 = 56.
  3. Put them together, and the answer is 5625.

In other words, take the digit(s) that go before the 5. Multiply that number by one higher (so for 45 you do 4 x 5, whereas for 325 you do 32 x 33). Stick 25 onto the end of this number, and hey presto, you’ve squared it!

Why does this work? Well, I’m a mathematician so I’ve written out the proof by hand:

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