MATHEMATICS 7 



There are as many figures preceding the decimal point in the 

 root 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 are 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, \.OG0442 = .021024, 

 ^518000 = 80.31 13, and ^.003073 = .04 18. 



If the number has more than three significant figures, point 

 off the number into periods, place a decimal point between the 

 first and second periods of the significant part of the number, 

 and proceed as in the following examples: 



EXAMPLE 1. Find the results of the following: 

 (a) \3.1416 = ? (b) A/2342.9 = ? 



SOLUTION. (a) In this case, the decimal point need hot 

 be moved. In the table under n 2 find 3.1329 = 1.77 2 and 

 3.1684 = 1.78 2 , one of these numbers being a little less and 

 the other a little greater than the given number, 3.1416. The 

 first three figures of the required root are 177. 31 ,684 - 31,329 

 = 355 is the first difference; 31,416 (the number itself) 31,329 

 = 87 is the second difference. 87 -4- 355 = .245, or .25, which 

 gives the fourth and fifth figures of the root. Hence, "V3.1416 

 = 1.7725. 



(b) Pointing off and placing the decimal point between 

 the first and second periods, the number appears 23.4290. 

 Under n 2 find 23.4256 = 4.84 2 and 23.5225 = 4.85 2 . The first 

 three figures of the root are 484. The first difference is 235,225 

 -234,256 = 969; the second difference is 234,290-234,256 

 = 34; 34-H969 = .035, or .0-4, which gives the fourth and fifth 

 figures of the root. Since the integral part of the number 

 23'42.9 contains two periods, the integral part of the root 

 contains two figures, or V2342.9 = 48.404. 



EXAMPLE 2. Find the results of the following: 

 (a) ^.0000062417 = ? (b) -$50932676 = ? 



SOLUTION. (a) Pointed off, the number appears .000'006'- 

 241'700, and with the decimal point placed between the first 

 and second periods of the significant parts, gives 6.2417. Under 

 n* find 6.22950=1.843 and 6.33163 = 1.853. The first three 

 figures of the root are 1.84. The first difference is 10,213. and 



