September 25th 2021 archive

Week 3 – Precalc 11

In precalc 11 class this week, we learned about adding and subtracting radical expressions. This involves combining like terms that are radicals. Like terms is something I had learned about before, but I didn’t realize it was possible with radicals. Terms are numbers, variables, and/or exponents in groups. Here are four examples of terms:

When the variables and exponents in more than one term are the same, the terms are “like”. The coefficients (number in front of the variable) can be different. For example:

When multiple radicands and their index are the same, they can be combined. For example, these radicals are like terms, because they have the same radicand and index (the square root of 4):

It is important to remember that the coefficient can be different for each term, because that is what’s being combined. To combine like terms, add/subtract the coefficients based on the sign in front of them. If there is no sign, it is positive. Here are the steps to combine like terms that are radicals:

If the radical has no number in front, there is an invisible coefficient of 1. Don’t forget to add or subtract it as well! Here is one final example: