This week in Precalc 11, we covered addition and subtraction of radicals
I learned that when we want to add or subtract 2 radicals, the radicand has to be the same.
The rules about adding and subtracting radicals are
The radicands and indexes must be the same, when we add or subtract, the radicand stays the same but the coefficient changes.
For example: This equation has the same radicand so we can simply just add the coefficients together. We DO NOT touch the index or radicand.
The radicands are the same so we can add them as seen below
Next question
When we want to add 2 radicals that are not simplified and in entire form with different radicands, we first simplify the radicand and turn it into a mixed radical. We then can add the 2 radicals if they have the same radicand. Here are the steps in picture.
For subtraction, we follow the same steps until the end. Instead of adding the coefficients, we subtract them.
Sometimes the radicands won’t end up being the same after we simplify them so the mixed radicands would be our final answer as seen below.
The bottom equation is our final answer.