How to Add and Subtract Radicals With Variables

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Just because a radical has variables doesn't make it any more difficult to add or subtract. Add and subtract radicals with variables with help from an expert in mathematics in this free video clip.

Part of the Video Series: Radical Numbers
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Video Transcript

Hey there. It's Dr. K with Infinite Magic Productions. And in today's tutorial we're going to learn how to add and subtract radicals with variables in the expression. So lets do some examples. The first equation that we're going to do, we're going to subtract radical X - 3 radical X. So when we're subtracting radicals we need to recognize that when we subtract them that this radical has the number 1 in front of it. So this expression is the same as saying 1-3*radical X. Because when you do the power of multiplication what you get is radical X*1-3*the radical X, or the original expression. This is just an easier way to see how we can simplify it. So 1-3 is going to equal -2* the radical X. That's the answer. So lets do another equation where we'll add slightly more complicated radicals. Here we're going to do radical of Y squared X radical of X. So in order to do this equation, the first thing we would want to do is to simplify our radicals. This radical right here has a squared variable in it. And therefore we can pull it out make it more simple. We can turn this into, we're going to pull the Y squared out, so it's going to turn into Y radical X plus radical X. So this is the simplest version or the answer to the equation. Now if you wanted to convert it into something slightly different you can also say that this is equal to, if you're going to pull the X outside of both of these, out of this equation, you're going to take radical X out. And this is going to turn into Y 1. And just recognize that when you multiply the radical X times this equation what you get is this right here. So either way, both of those answers are correct. And there you have it. That's how you add or subtract radicals with different variables in them. Thanks for watching, I'm Dr. K.


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