CUBE ROOT 



1663 



CUBE ROOT 



PARTS OF 



Fig. a, at left, represents the cube of the tens ; 

 the units, taken three times ; Fig. c, right center, 

 d, at right, the cube of the units. 



(4) nxnxn = 27. 



What number used as a factor 3 times gives 

 27? 



n= 6. 



6 used 3 times as a factor gives 216or6X6X 

 6 = 216. 



(6) n 3 = 27; 

 n 3. 



This is read, "What number cubed gives 27?" 

 "3 cubed gives 27, or, 

 3X3X3 = 27." 



(7) ^TJ3. 



This is read, "The cube root of 27 is 3." 



Cube and Cube Root of Common Fractions. 

 Following are examples illustrating this phase 

 of cube root: 



\y = 2 X 2 X 2 = 8 



27 



"1000' 



The cubes of the tens from 10 to 90 can be 

 easily learned by memorizing the cubes from 

 1 to 9. 



1=1. 10*=1000. 



2 3 = 8. 20=8000. 



3 3 =27. 30 3 =r27000. 



4'=64. 40'=64000. 



5*=125. 50=125000. 



6=216. 60 = 216000. 



7 3 =343. 70=343000. 



8=512. 80=512000. 



9 3 =729. 90 3 =729000. 



A CUBE 



Fig. b, left center, the square of the tens times 

 the tens times the units, taken three times ; Fig. 



Cube and Cube Root of Decimal Fractions. 

 The cube of the decimal fraction offers no 

 new difficulty. A product contains as many 

 decimal places as all its factors contain; for 

 example, .6 X. 6 X. Q= .216. Therefore, from the 

 above we have: 



.1 3 =.001. 

 .2=.008. 



.5 3 =.125. 



.01 3 = . 000001. 

 .04*=. 000064. 

 .09*=.000729. 



^7729"=. 9. 



In all the above problems it is possible to 

 get the cube root at sight or by a little careful 

 inspection. 



Cube Root by Factoring. The next simple 

 method is that of factoring where the three 

 equal factors are not so apparent. For ex- 

 ample : 



(1) 



15625 = 5X5X625. 

 5X5X625 = 5X5X5X125. 

 5X5X5X125 = 5X5X5X5X25. 

 ^15625 = 25X25X25. 



(2) 



4096 = 4X1024. 

 4X1024 = 4X4X256. 

 4X4X256 = 4X4X16X16. 

 ^4096 = 16X16X16. 



We can find the cube root of an indicated 

 product by factoring. For example, "What 

 is the edge in inches of a cubic space whose 

 capacity is 8 cubic feet?" 

 Volume in cubic inches = 8x 1728. 

 Edge in inches= ^8X1728 = 



7^(2X2X2)X(12X12X12). 

 Edge in inches = 2X 12 = 24. 

 f 27X216=^3X3X3X6X6X6 = 3X6 = 18. 

 ^512X343 = 8X7 = 56. 

 ^7 29 XI 25 = 9X5 = 45. 



The above problems are all solved more or 

 less freely by inspection. 



