MATHEMATICS 27 



number and the given number; divide the second difference 

 by the first difference, carrying the quotient to three decimal 

 places and increasing the second figure by 1 if the third 

 is 5 or a greater digit. The two figures of the quotient 

 thus determined will be the fourth and fifth figures of the 

 root. In the present example, dropping decimal points, 

 in the remainders, 3.1684-3.1329 = 355, the first difference; 

 3.1416-3.1329 = 87, the second difference; 87-*-355 = .245 + , 

 or .25. Hence, "Nf37l416 = 1.7725. 



(b) \2342.9 =? Pointed off into periods, the number 

 appears as 23'42.90, and by moving the decimal point, the 

 number appears as 23.4290; the first three figures of the root 

 are 484; the first difference is 23.5225-23.4256 = 969; the 

 second difference is 23.4290-23.4256 = 34; 34 H- 969 = .035 + , 

 or .04. Hence, A/2342. 9 = 48. 404. 



Cube Root. The cube root of a number is found in the 

 same manner as the square root, except the given number is 

 pointed off into periods of three figures each. The following 

 numbers would be pointed off thus: 3141.6, 3'141.6; 

 67296428, 67'296'428; 601426.314, 60F426.314; .0000000217, 

 .000'000'021'700. 



Having pointed off, move the decimal point so that it will 

 fall between the first and second periods of the significant 

 part of the number, as in square root. In the above 

 numbers the decimal point will be placed thus: 3.1416, 

 67.296,428, 601.426314, and 21.7. 



If the given number has but three (or less) significant 

 figures, find the significant part of the number in the 

 column headed n\_ the cube root will be found in the column 

 headed 3ln, ^10n, or ^lOOn, according to whether one, 

 two, or three figures precede the decimal point after it has 

 been moved. Thus, the cube root of 21.7 will be found oppo- 

 site 2.17, in column headed ^T6n, while_the cube root of 2.17 

 will be found in the column headed "Vn, and the cube root 

 of 217 in the column headed "^lOOn, all on the same line. 

 If the given number contains more than thr.ee significant 

 figures, proceed exactly as described for square root, but use 

 the column headed n 3 . 



EXAMPLE. (a) ^.0000062417 = ? (&) ^50932676^=? 



