If we take a number and multiply it by itself we call the result the square of the number. The process is called squaring the number. If we find the number which, when multiplied by itself is equal to a given number, the former number is called the square root of the given number. The process is called extracting the square root of the number. Both these processes may be carried out on the A and D scales of a slide rule. For example: Example 27: 4 * 4 = square( 4 ) = 16 Set indicator over 4 on D scale. Read 16 on A scale under hair-line. Example 28: square( 25.4 ) = 646.0 The decimal point must be placed by mental survey. We know that square( 25.4 ) must be a little larger than square( 25 ) = 625 so that it must be 646.0. To extract a square root, we set the indicator over the number on the A scale and read the result under the hair-line on the D scale. When we examine the A scale we see that there are two places where any given number may 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.