 This video will talk about simplifying radicals. When we simplify radicals, you kind of first have to think about squaring. So if we have 5 squared, that's equal to 25, and if we have negative 5 squared, that's supposed to be equal to 25 as well. But when you take the square root then, it's kind of doing it squaring backwards. You're going to unsquare 25 in this case. So we would take the square root of 25, and we take the square root of 25 and we get 5. If we had the negative square root of 25, it would also be 5. The first one we use is called the principal root. If you're going to take the square root of something, you're usually going to give the principal root. The second one is called the negative root. If you have a negative in front, then we're taking the negative root. So let's look at several examples here, and we'll start here with these. The square root of 64. So I'm really saying, what squared is equal to 64? When I do that, I would have, we could say the 8 squared is 64. So then we could say, this is the same thing as the square root of 8 squared, and we all know that the square root cancels each other out, and we're just left with 8. So if I look at the next one, I want the opposite of the square root of something squared being 16. So what squared is going to give me 16? That would be 4 squared is equal to 16. So I want the square root of 4 squared, which is the same thing as just 4, because the square and the square root undo each other. And finally, now we have one that's got a fraction underneath of it. But you can just simplify the fraction. You can think of this as the square root of 9 over the square root of 25. And if you take that, the square root of 9 would be 3 without a radical, and the square root of 25 would be 5 without a radical. So we have 3 fifths. All right, let's move on to cube roots. When we talk about cube roots, we need to just find out something times itself that, three times, that gives us our number. So if we have two times itself, three times, we get 8. So the cube root of 8 is really the cube root of 2 cubed or 2. And now, watch, when you have a cube root, we can have a negative number times itself three times and still gives us a negative. So this is actually wrong. It should say negative 2 cubed would be negative 8. And the cube root of negative 8 would be negative 2. So if I have a negative underneath my radical, that tells me that my answer is going to be equal to a negative number. And I think negative 3 times negative 3 times negative 3. This gives me, these two give me positive 9 times negative 3, which is negative 27. So the cube root of negative 27 is negative 3. Now this time, I really want the opposite of the cube root of something cubed that gives me 125, and that would be 5 cubed. So the cube and the cube root cancel each other out. So I still have the negative out front, and I have the 5. So it would be negative 5. And finally, the cube root of 64, what times itself three times? So an accidently to the square root, we want to know the cube root of what cubed would give us 64, and that's going to be 4 cubed. So in here, we would say 4 cubed, and the cube root, and the cube cancels each other out, so the cube root of 64 is 4. Now of course, we could have always done these with our calculator. But we wanted to make sure that you got the concept of how they work. But now, if we go back to the calculator, let me get my calculator all cleared up here. If I wanted to do a square root, the keystrokes would be the second, and then the x squared, above that you see a square root. So the square root of, and let's do the 25 that we began this problem with. So the square root of 25, and then close my parentheses, press Enter, and I find out that sure enough it's 5. And if we want to do a cube root, we have to do one extra step. We have to go under Math, and then you see here at 4, it says cube root. So we would say, we would net number 4, and that gives me this cube root. And now I get to put my number in, so let's do the 64 that we just ended with. And if I do the cube root of 64, sure enough, it's 4. And just to show you the other two, practice the cube root, because that one's a little bit different. The negative, and then the cube root under Math, option 4. The negative cube root of 125, I should get negative 5, and sure enough, we do. And then finally, the cube root, go back to Math, number 4. And we want to put in our negative 27, close the parentheses, and we find out that we get negative 3. So you could do this with a calculator. But if we want you to show work, you would want to show that you were taking the cube root of something cubed, or the square root of something squared.