From the Fun Fact files, here is a Random Fun Fact, at the Advanced level: Squaring Quickly
You may have seen the Fun Fact on
squares ending in 5;
Here's a trick that can help you square ANY number quickly.
It's based on the algebra identity for the difference of squares, but with a twist! Can you figure
it out?
54^{2} = 50 * 58 + 4^{2} = 2916.
42^{2} = 40 * 44 + 2^{2} = 1764.
37^{2} = 34 * 40 + 3^{2} = 1369.
You have to pretty proficient at multiplying one digit
numbers by two digit numbers in your head
to do this trick well. But
if you master this, then you can build upon it in some
amazing ways:
116^{2} = 100 * 132 + 16^{2}
= 13,200 + 256 = 13,456.
Thinking CREATIVELY about everything you learn, no matter
how trivial it may seem, will allow you to find some
really clever applications!
Presentation Suggestions:
If you practice this a LOT beforehand, you can start
off by asking students to name any 2digit number and you
will do it in your head quickly. Then tell them the trick.
But only do this with a LOT OF PRACTICE!
The Math Behind the Fact:
If you look closely, we are using the identity:
a^{2} = (ab)(a+b) + b^{2}.
The reference contains more ideas for doing
fast mental calculations. See also Fun Facts on lightning arithmetic.
How to Cite this Page:
Su, Francis E., et al. "Squaring Quickly."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
The Link for this Fun Fact:
is directly accessible here.
