secrets-of-mental-math-malestrom

120
Secrets of Mental Math
roots. In practice, you only need to look at the square root of
the first two digits of six-digit numbers (or the first digit of five
numbers). Once you figure out that the square root of 59 lies
between 7 and 8, you know your answer is in the 700s.
Now proceed in the usual manner:
Divide:
847
700593472
ª
847
75934
Average:
700 847
2
773.5
The exact square root of 593,472 is 770.37 (to five places),
so you’re pretty close. But you could have been closer, as the following
trick demonstrates. Note that the first two digits, 59, are
closer to 64 (8 8) than they are to 49 (7 7). Because of this
you can start your guesstimation with the number 8 and proceed
from there:
Divide:
741
800593472
ª
741
85934
Average:
800 741
2
770.5
Just for fun, let’s do a real whopper—the square root of
28,674,529. This isn’t as hard as it might seem. Your first step is
to round to the nearest large number—in this case, just find the
square root of 29.
Divide:
5.8
529.0
25
40
Average:
5 5.8
2
5.4