Squares Ending in 5

Give me any 2 digit number that ends in 5, and I’ll square it in my head! 
452 = 2025 
852 = 7225, etc.

There’s a quick way to do this: if the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1).

Presentation Suggestions:
After telling the trick, have students see how fast they can square such numbers in their head, but doing several examples.

The Math Behind the Fact:
You may wish to assign the proof as a fun homework exercise: multiply (10N+5)(10N+5) and interpret! The trick works for larger numbers, too, although it may be harder to do this in your head. For instance 2052 = 42025, since 20*21=420. Also, you can combine this trick with other lightning arithmetic tricks. So 1152 = 13225, because 11*12 = 132, using the Multiplication by 11 trick.

The reference also contains more secrets of fast mental calculations.

How to Cite this Page: 
Su, Francis E., et al. “Squares Ending in 5.” Math Fun Facts. <https://www.math.hmc.edu/funfacts>.

A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006.

Fun Fact suggested by:
Francis Su

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