y be set, so we must have some way of deciding in a given case
which half of the A scale to use. The rule is as follows:

(a) If the number is greater than one. For an odd number of digits to
the left of the decimal point, use the left-hand half of the A scale.
For an even number of digits to the left of the decimal point, use the
right-hand half of the A scale.

(b) If the number is less than one. For an odd number of zeros to the
right of the decimal point before the first digit not a zero, use the
left-hand half of the A scale. For none or any even number of zeros to
the right of the decimal point before the first digit not a zero, use
the right-hand half of the A scale.

Example 29: square_root( 157 ) = 12.5

Since we have an odd number of digits set indicator over 157 on
left-hand half of A scale. Read 12.5 on the D scale under hair-line. To
check the decimal point think of the perfect square nearest to 157. It
is

12 * 12 = 144, so that square_root(157) must be a little more than 12 or
12.5.

Example 30: square_root( .0037 ) = .0608

In this number we have an even number of zeros to the right of the
decimal point, so we must set the indicator over 37 on the right-hand
half of the A scale. Read 608 under the hair-line on D scale. To place
the decimal point write:

square_root( .0037 ) = square_root( 37/10000 )
= 1/100 square_root( 37 )

The nearest perfect square to 37 is 6 * 6 = 36, so the answer should be
a little more than 0.06 or .0608. All of what has been said about use of
the A and D scales for squaring and extracting square root applies
equally well to the B and C scales since they are identical to the A and
D scales respectively.

A number of examples follow for squaring and the extraction of square
root.

Example
31: square( 2 ) = 4
32: square( 15 ) = 225
33: square( 26 ) = 676
34: square( 19.65 ) = 386
35: square_root( 64 ) = 8
36: square_root( 6.4 ) = 2.53
37: square_root( 498 ) = 22.5
38: square_root( 2500 ) = 50
39: square_root( .16 ) = .04
40: square_root( .03 ) = .173

CUBING AND CUBE ROOT

If we take a number and multiply it by itself, and then multiply the
result by the original number we get what is called the cube of the
original number. This process is called cubing the number. The reverse
process of finding the number which, when multiplied by itself and then
by itself again, is equal to the given number, is called extracting the
cube root of th