How do you divide radicals with variables?

1 Answer
Apr 12, 2015

If you have two radicals that are being operated on with the same degree (that is, if both are square roots, both are cube roots, etc.), you can combine them under one big radical symbol. Then you can divide as normal, and ignore the effects of the radical.

For example:

#sqrt(x^2 - 4)/sqrt(x+2) = sqrt((x^2-4)/(x+2)) = sqrt(((x+2)(x-2))/(x+2))) = sqrt(x-2)#


#sqrt(x-2)/sqrt(x^2 - 4) = sqrt((x-2)/(x^2 - 4)) = sqrt((x-2)/((x+2)(x-2)))) = sqrt(1/(x+2))#