# Algebra - Roots

Bases :a,b
Powers (retional numbers) :n,m
a,b$\geq$0 foreven roots (a=2k, k $\in$N

1. $\sqrt[n]{ab}= \sqrt[n]{a}\sqrt[n]{b}$
2. $\sqrt[n]{a}\sqrt[m]{b}= \sqrt[nm]{a^mb^n}$
3. $\sqrt [n]{b^2 \over b}={\sqrt[n]a \over \sqrt[n]b }, b \neq0$
4. ${\sqrt[n]a \over \sqrt[m]b }={\sqrt[nm]a^m \over \sqrt[nm]b^n }=\sqrt [nm]{a^m \over b^n},b \neq 0$
5. $(\sqrt[n]{a^m})^p= \sqrt[n]{a^{mp}}$
6. $(\sqrt [n]{a^m})^p=\sqrt[n]{a^{mp}}$
7. $\sqrt[n]{a^m}=a^{m \over n}$
8. $\sqrt [m]{\sqrt[n]{a}}=\sqrt [mn]{a}$
9. $(\sqrt[n]{a})^m=\sqrt [n]{a^m}$
10. ${1 \over {\sqrt[n]{a}}}={\sqrt[n]{a^{n-1}} \over a} , a \neq 0.$
11. $\sqrt {a \pm \sqrt {b}}=\sqrt {a+\sqrt{a^2-b}\over 2} \pm \sqrt {a-\sqrt{a^2-b}\over 2}$
12. ${1 \over {\sqrt{a}} \pm \sqrt{b}}={{\sqrt{a} \mp \sqrt{b}} \over {a-b}}$