What are the two steps for simplifying radicals? Can either step be deleted? If you could add a step that might make it easier or easier to understand, what step would you add?



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Posted on (Answer #1)

I teach 3 steps/rules for simplifying radicals:

(1) There can be no fractions in the radicand.

Use the "rule" `sqrt(a/b)=sqrt(a)/sqrt(b)` (True for any index -- thus `root(3)(a/b)=(root(3)(a))/(root(3)(b))` etc...)

(2) There can be no radicals in the denominator.

Use conjugation to clear the radical from the denominator.


This is somewhat complicated for other indices. We multiply both numerator and denominator by a radical that creates a perfect nth power in the radicand of the denominator where n is the index.


(3) There can be no perfect nth powers in the radicand where n is the index.



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