26 MATHEMATICS 



It will be more convenient to explain first how to use the 

 table for finding square and cube roots. 



Square Root. First point off the given number into periods 

 of two figures each, beginning with the decimal point and 

 proceeding to the left and right. The following numbers 

 are thus pointed off: 12703, 1'27'03; 12.703, 12.70'30; 

 220000, 22'00'00; .000442, .00'04'42. 



Having pointed off the number, move the decimal point 

 so that it will fall between the first and second periods of the 

 significant part of the number. In the preceding numbers, 

 the decimal point will be placed thus: 1.2703, 12.703. 

 22., 4.42. 



If the number has only three (or less) significant figures, 

 find the significant part of the number in the column headed n ; 

 the_square root will be found in the column headed \n or 

 "VlOw, according to whether the part to the left of the 

 decimal point contains one figure or two figures. Thus, 

 ^4^42 = 2.1024, and \22= A/10 X 2.20 = 4.6904. The decimal 

 point is located in all cases by reference to the original 

 number after pointing off into periods. 



There will be as many figures in the root preceding the decimal 

 point as there are periods preceding the decimal point in the 

 given number; if the number is entirely decimal, the root is 

 entirely decimal, and there will be as many ciphers following the 

 decimal point in the root as there are cipher periods following 

 the decimal point in the given number. 



Applying this rule, -^220000 = 469. 04 and \.000442 

 = .021024. 



The operation when the given number has more than 

 three significant figures is best explained by an example. 



EXAMPLE. (o) V3.1416=? (&) ^2342.9 = ? 



SOLUTION. (a) Since the first period contains only one 

 figure, there is no need of moving the decimal point. Look 

 in the column headed n 2 and find two consecutive numbers, 

 one a little greater and the other a little less than the given 

 number; in the present case, 3.1684 = 1.78 2 and 3.1329 = 1.77 2 . 

 The first three figures of the root are therefore 177. Find the 

 difference between the two numbers between which the 

 given number falls, and the difference between the smaller 



