Instruction for Using a Slide Rule | Page 4

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: squareroot( 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 squareroot(157) must be a little more than 12 or 12.5.
Example 30: squareroot( .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:
squareroot( .0037 ) = squareroot( 37/10000 ) = 1/100 squareroot( 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: squareroot( 64 ) = 8 36: squareroot( 6.4 ) = 2.53 37: squareroot( 498 ) = 22.5 38: squareroot( 2500 ) = 50 39: squareroot( .16 ) = .04 40: squareroot( .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: cuberoot( 185 ) = 5.70
Since there are 3 digits in the given number, we set the indicator on 185 in the right-hand third of the K scale, and read the result 570 on the D scale. We can place the decimal point by thinking of the nearest perfect cube, which is 125. Therefore, the decimal point must be placed so as to give 5.70, which is nearest to 5, the cube root of 125.
Example 42: cuberoot( .034 ) = .324
Since there is one zero between the decimal point and the first digit not zero, we must set the indicator over 34 on the middle third of the K scale. We read the result 324 on the D scale. The decimal point may be placed as follows:
cuberoot( .034