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 the given number. Thus, since 5 * 5 * 5 = 125, 125 is the
cube of 5 and 5 is the cube root of 125.

To find the cube of any number on the slide rule set the indicator over
the number on the D scale and read the answer on the K scale under the
hair-line. To find the cube root of any number set the indicator over
the number on the K scale and read the answer on the D scale under the
hair-line. Just as on the A scale, where there were two places where you
could set a given number, on the K scale there are three places where a
number may be set. To tell which of the three to use, we must make use
of the following rule.

(a) If the number is greater than one. For 1, 4, 7, 10, etc., digits to
the left of the decimal point, use the left-hand third of the K scale.
For 2, 5, 8, 11, etc., digits to the left of the decimal point, use the
middle third of the K scale. For 3, 6, 9, 12, etc., digits to the left
of the decimal point use the right-hand third of the K scale.

(b) If the number is less than one. We now tell which scale to use by
counting the number of zeros to the right of the decimal point before
the first digit not zero. If there are 2, 5, 8, 11, etc., zeros, use the
left-hand third of the K scale. If there are 1, 4, 7, 10, etc., zeros,
then use the middle third of the K scale. If there are no zeros or 3, 6,
9, 12, etc., zeros, then use the right-hand third of the K scale. For
example:

Example 41: cube_root( 185 ) = 5.70
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