# Thread: Property of Radicals

1. ## Property of Radicals

Since $\sqrt[m]{\sqrt[n]{b}} = \sqrt[mn]{b}$, how would you be able to simplify $\sqrt[m]{a\sqrt[n]{b}}$ where a and b​ are both constants

2. ## Re: Property of Radicals

Rene

Very simple....the variable a enters the radical and gets a power n the rest is easy.
The final answer is (mn) root(a^n x b) .

3. ## Re: Property of Radicals

1 remove the inner radical sign giving a*b^1/n
2 remove the outer radical sign giving a^1/m*b^1/mn

4. ## Re: Property of Radicals

Originally Posted by ReneG
Since $\sqrt[m]{\sqrt[n]{b}} = \sqrt[mn]{b}$, how would you be able to simplify $\sqrt[m]{a\sqrt[n]{b}}$ where a and b​ are both constants
You could write it as $\sqrt[m]{a}\sqrt[mn]{b}$ or as $a^{1/m}b^{1/mn}$