Give me any 2 digit number that ends in 5, and I'll square
it in my head!
45^{2} = 2025
85^{2} = 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
205^{2} = 42025,
since 20*21=420. Also, you can combine this trick with
other lightning arithmetic tricks. So
115^{2} = 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>.
