New School Algebra

Cover New School Algebra
New School Algebra
George Albert Wentworth
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^"^ 2. (a^A^)^ 11. (a;2-2)*.
6 2VY ^^- (•^ + 3)'- 3 a^»V ^ 13. (2 X 4- 1)«. /'' 4. {-^ab'^cyry 14. (2//i2-l)5.
5. (-Txhjzy. 15. (2a; + 3 2/)^ 16. (2a;-2/)«.
17. (a-y-2)^/.
7. (-2a;y)6. 18. (1 - a; + a;^)^.
8. (- 3 a^^'xy, 19. (1 - 2 a; + 3 x^, 20. (l-.a-ha^)^ ^' 21. (3-4.x + 5xy, Evolution.
/ 3aWY / 3a;y Y 223. The operation of finding any required root of an expression is called Evolution. A root of an imperfect power cannot be found exactly.
Thus, the exact value of the square root of 2 can b
...e written only as V^, and the exact value of the cube root of 4 can be written only as vi. Approximate values of these expressions, however, can be found by annexing ciphers and extracting the root.
216 INVOLUTION AND EVOLUTION, 824. Index Law for Evolution. If m and n are positive integers, we have (a«)« = a"»« (§ 215) (/onversely, Va*"" = a » = a™.
Also, (a*)" = a%\ (§ 216) C'Onversely, Va^ = Va" X V^ = ab, and Vo^ = Va X Vb, Thus, the ^ root of a* is a* = a^ ; the fourth root of 81 a^* is found by taking the fourth root of 81 and of a"; and is 3 a* Hence, 225.


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