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. <http://www.math.hmc.edu/funfacts>.

References: A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006. Keywords:    lightning arithmetic Subjects:    algebra Level:    Easy Fun Fact suggested by:   Francis Su Suggestions? Use this form. 4.26 current rating Click to rate this Fun Fact...     *   Awesome! I totally dig it!     *   Fun enough to tell a friend!     *   Mildly interesting     *   Not really noteworthy and see the most popular Facts! Get the Math Fun Facts iPhone App!

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!