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Root -Algebra Formulas

Root formulas

Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.

Bases : a, b

Powers (rational numbers) : n, m

a,b ≥ for even roots(n = 2k, k ∈ N)

1. abn=anbn 1.\ \sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}
2. anbm=ambnnm 2.\ \sqrt[n]{a} \sqrt[m]{b} = \sqrt[nm]{a^mb^n}
3. abn=anbn,b≠0 3.\ \sqrt[n]{\frac ab} = {\sqrt[n]{a} \over \sqrt[n]{b}}, b \neq 0
4. anbn=amnmbnnm=ambnnm,b≠0 4.\ {\sqrt[n]{a} \over \sqrt[n]{b}} = {\sqrt[nm]{a^m} \over \sqrt[nm]{b^n}} = \sqrt[nm]{\frac {a^m}{b^n}} , b \neq 0
5. (amn)p=ampn 5.\ ( \sqrt[n]{a^m} )^p = \sqrt[n]{a^{mp}}
6. (an)n=a 6.\ ( \sqrt[n]{a} )^n = a
7. amn=ampnp 7.\ \sqrt[n]{a^m} = \sqrt[np]{a^{mp}}
8. amn=amn 8.\ \sqrt[n]{a^m} = a^{\frac mn}
9. anm=amn 9.\ \sqrt[m]{\sqrt[n]{a}} = \sqrt[mn]{a}
10. (an)m=amn 10.\ ( \sqrt[n]{a} )^m = \sqrt[n]{a^m}
11. 1an=an–1na,a≠0 11.\ {1 \over \sqrt[n]{a}} = {\sqrt[n]{a^{n-1}} \over a}, a \neq 0
12. a±b=a+a2–b2±a–a2–b2 12.\ \sqrt{a \pm \sqrt{b}} = \sqrt{\frac {a + \sqrt{a^2 – b}}{2}} \pm \sqrt{\frac {a – \sqrt{a^2 – b}}{2}}
13. 1a±b=a±ba–b 13.\ {1 \over \sqrt{a \pm \sqrt{b}}} = {\sqrt{a} \pm \sqrt{b} \over a-b}
14. an=a1n 14.\ \sqrt[n]{a} = a^{\frac 1n}

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