# Property of Radicals

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• June 15th 2013, 01:46 AM
ReneG
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
• June 15th 2013, 02:54 AM
MINOANMAN
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) .
• June 15th 2013, 06:31 AM
bjhopper
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
• June 15th 2013, 08:35 AM
HallsofIvy
Re: Property of Radicals
Quote:

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 $a^{1/m}b^{1/mn}$