Elements of Algebra

CHAP. IX. OF ALGEBRA. 109 $a^6-6a^5+15a^4-20a^3+15a^2-6a+1(a^2-2a+1$ $a^6$ --- $3a^4-6a^3+4a^2) -6a^5+15a^4-20a^3$ $-6a^5+12a^4-8a^3$ --- $3a^4-12a^3+12a^2+3a^2-6a+1) 3a^4-12a^3+15a^2-6a+1$ $3a^4-12a^3+15a^2-6a+1$ --- $0.$ 339. The analysis which we have given is the foundation of the common rule for the extraction of the cube root in numbers. See the following example of the operation in the number 2197: $2197(10+3=13$ $1000$ --- $300 | 1197$ $90$ $9$ --- $399 | 1197$ --- $0.$ Let us also extract the cube root of 34965783: $34965783(300+20+7$, or $327$ $27000000$ --- $270000 | 7965783$ $18000$ $400$ --- $288400 | 5768000$ --- $307200 | 2197783$ $6720$ $49$ --- $313969 | 2197783$ --- $0.$