0 upvotes, 0 direct replies (showing 0)
View submission: Ask Anything Wednesday - Engineering, Mathematics, Computer Science
Yeah, this holds up, and is actually a specific example of a more general principle.
If we think of things a little differently
(a-x) * (a+x) = a^2 - x^2
So in your example
(5.5-.5) * (5.5+.5) = 30.25 - .25
(5.5-1.5) * (5.5-1.5) = 30.25 - 2.25
2.25 - .25 = 2
That's where your 2 is coming from!
You could take this farther
(5.5+2.5) * (5.5-2.5) = 30.25 - 6.25
And sure enough 8×3 is 24
I use this pretty frequently to estimate squares and square roots in my head.
For example if I want know what 6.666^2 is I can do
(6.666-.666) * (6.666+.666) =
6 * 7.333 = 44
44 = 6.666^2 + .444
6.666^2 = 44.444
Edit: oops subtracted at the end instead of added
There's nothing here!