Root Formulas, Algebra

Posted In: Mathematics

Bases: a,b
Powers (rational numbers): m,n
$a,b≥0$ for even roots (n=2k, k∈N)

  1. $√^n{ab}=√^na.√^nb$
  2. $√^na.√^mb=√^{nm}{a^mb^n}$
  3. $√^n{a/b}={√^na}/{√^nb}$, b≠0
  4. ${√^na}/{√^mb}={√^{nm}a^m}/{√^{nm}b^n}={√^{nm}{a^m/b^n}$, b≠0
  5. $(√^na^m)^p=√^na^{mp}$
  6. $√^na^n=a$
  7. $√^na^m=√^{np}a^{mp}$
  8. $√^na^m=a^{m/n}$
  9. $√^m{√^na}=√^{mn}a$
  10. $(√^na)^m=√^na^m$
  11. $1/√^na={√^na^{n-1}}/a, a≠0$
  12. $√{a±√b}=√{{a+√{a^2-b}}/2}±√{{a-√{a^2-b}}/2}$
  13. $1/{√a±√b}={√a∓√b}/{a-b}$

Post Tags: Algebra


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