Simplifying Radicals

by Julisa Gallegos


A square root is radical. A radical is a root of a number. A square root is a radical. Roots can be square roots, cube roots, fourth roots, ect. When simplifying a radical, you create factor trees, and depending on the end result is how many numbers go outside/inside of the radical; as well as how many pairs or triplets it contains.


When simplifying radicals with square roots, you are to make a factor tree and look for pairs in the results, the pairs will go on the outside of the radical and the leftovers will go inside. Whenever a radical is left blank, it is a squared root

Example : Square Roots

In this problem, the 175 is being simplifying into 25 and 7, then the 25 is simplified into 5 and 5. Once the problem is completely broken down and simplified like now, you look for pairs which in this case would be 5 and 5. Those pairs would go on the outside of the radical symbol and the pairless

left over numbers will go inside the radical symbol, which in this case, its 7.

Example : Cubed Roots

In this problem we are given negative 1000 inside the radical, which splits into negative 10 and positive 100. From those numbers, we find a triplet of negative 2's and a triplet of positive 5's. Which leaves our answer at -2 x 5 = -10.


When simplifying cubed roots, you repeat the same process with square roots, but instead you're looking for triplets this time. And this time, the radical contains a three. Often times, cubed roots can contain negative numbers inside the radical symbol, which can result in a negative answer.

Simplify Square Roots and Cube Roots