secrets-of-mental-math-malestrom

Math for the Board: Pencil-and-Paper Math 135
answer. The key is to subtract the mod sums you arrive at and
then compare that number to the mod sum of your answer:
65,717 8
3 8 , 4 9 1
7
27,226 1
19 10
There’s one extra twist. If the difference in the mod sums is a
negative number or 0, add 9 to it. For instance:
42,689 2
1 8 , 7 6 4
8
23,925 6 9 3
21
3
PENCIL-AND-PAPER SQUARE ROOTS
With the advent of pocket calculators, the pencil-and-paper
method of calculating square roots has practically become a lost
art. You’ve already seen how to estimate square roots mentally.
Now I’ll show you how to do it exactly, using pencil and paper.
Remember how in guesstimating square roots you calculated
the square root of nineteen? Let’s look at that problem again, this
time using a method that will give you the exact square root.