CUBE ROOT 



1665 



CUBIC MEASURE 



3x70* =14700 

 3X70X2= 420 



15124 



Separate the number into periods of three digits 

 each, beginning at the right. Find the largest 

 cube in the first period, 373. It is 343. Place 

 its cube root, 7, in the answer. Subtract the 

 largest cube, 343, and bring down the next period. 

 Divide the remainder by three times the square 

 of the tens (in this case 3 X70 2 = 14700), and 

 place the quotient (2 in this case) in the answer 

 beside the number already there ; in this case this 

 gives 72 in the cube root. Then add to the trial 

 divisor (as 3 X tens 2 is called) three times the 

 tens times the units, which in this case is 3X70 

 X2 = 420, and add also the square of the units, 

 which in this case is 4. Then multiply the sum 

 of these three, which is the real divisor, in this 

 case 15124, by the units, which in this case is 2, 

 and place the product under the dividend. The 

 product, 30248, is the same as the dividend, and 

 72 is the cube root of 373248. 



Another illustration, when there are three digits 

 in the root : 



572 



187149248 

 125 



3X50 2 =7500 



3X50X 7 = 1050 



7 Z = 49 



8599 



3X570 2 =974700 



3X570 X2 = 3420 



2 2 = 4 



62149 



60193 



1956248 



1956248 



978124 



The only new point in this problem is that 57 

 becomes the tens at the second division, and the 

 divisor, 3 X tens 2 , becomes 3X570 2 . 



Cube Root of Decimals. In taking the cube 

 root of a number containing a decimal, we 

 separate it into periods, beginning at the deci- 

 mal point, and marking off into periods of 

 three digits each, to the left for the whole 

 number and to the right for the decimal, as, 



67'842.368'795. 



If the decimal part has not 3, 6, or 9, etc., 

 places, zeros are added, as : 



32.687'49. 

 32.687'490. 



The cube root of a decimal has % as many 

 decimal places as the cube has. The cube is 

 the product of three equal factors; there- 

 fore, it contains three times as many decimal 

 places as the cube root. If a given number 

 105 



is not a perfect cube, annex decimal zeros, in 

 groups of threes; carry it out as many decimal 

 places as is desired. For example: 



^70 = f 750.000'000'000, 



which will give the cube root to three decimal 

 places. 



Cube Root of Common Fractions. This is 

 touched upon in the early part of the article, 

 but we shall generalize it here: 



888 8 3 512" 



A 3 /343 1 ? / 343 7 

 Therefore, Vjjg.-gg-g. 



The cube root of a common fraction is a 

 fraction whose numerator is the cube root of 

 the numerator of the first fraction, and whose 

 denominator is the cube root of the denom- 

 inator of the first fraction, as, 



343 



T 



A.H. 



CUBIC, ku'bic, MEASURE, the system 

 used in the measurement of solids, that is, 

 bodies having the three dimensions of length, 

 breadth and thickness. It derives its name 

 from the cube, which is the unit of measure 

 employed in finding the contents, or volume, 

 of solids (see CUBE). The volume of a regular 

 solid is found by multiplying together the 

 numbers representing its three dimensions. 



Practical Applications. The following table, 

 which should be memorized, contains the 

 values commonly used in the solution of prob- 

 lems based on the cube: 



1728 cubic inches (cu.in.) =1 cubic foot (cu. ft.). 

 27 cubic feet =1 cubic yard (cu.yd.). 



231 cubic inches =1 gallon. 



2150.4 cubic inches =1 bushel. 



24 % cubic feet = 1 perch of stone. 



(a) How many cubic yards will be taken out 

 in digging a cellar 15 feet wide, 40 feet long and 8 

 feet deep? 



(b) What will it cost to build a stone wall 30 

 rods long, 3% feet high and 1 yard thick, at $6.50 

 a perch? 



(c) How many bushels of oats will a bin hold 

 which is 2 yards long, 2 % feet wide and 5 feet, 4 

 inches high? How many gallons of water would 

 a tank of equal size contain? 



Short Methods. The following rules will be 

 found helpful in the quick solution of various 

 practical problems: 



(1) To find the number of cubic feet in a log 

 multiply one-fourth of the average circumference 

 by itself and multiply the product obtained by the 

 length 1 , which will give the contents in cubic feet. 



(2) A full-sized cord of wood is a solidly-built 

 pile 8 feet long, 4 feet wide and 4 feet high, con- 

 taining 8 X 4 X 4, or 128, cubic feet. 



