 In this video, I'm going to talk about estimating square roots. So when we look at square roots, sometimes when we want to take the square root of a number, you don't necessarily need to know exactly what it is. You want to kind of find an estimate. So you better understand what's going on with the square roots. And so estimation is a good way to better understand a square root. So this is what we're doing. We're estimating the following radicals to the nearest tenth. So we're just going to go to one decimal place. We're not going to worry about two or three decimal places. That's really too much that we can do mentally. So we're just going to worry about one decimal place. OK, now the square root of 27. Now you look at that. You don't really know what the square root of 27 is, but we can estimate. We can take an estimated guess to see what that is. Now to find the estimated square root of the square root of 27, what we can do is think about the perfect squares that are around 27. So notice 25 and 36 are around 27. We actually know what the square root of 25 and the square root of 36. We actually know what those are. The square root of 25 is 5, and the square root of 36 is 6. So we know what those are. So that means 27 is going to be somewhere in between 5 and 6. Now depending how close this number is to 25 or to 36, that's going to tell us kind of how close this number is to 5 or to 6. Now looking at this number, 25 to 27, there's only two digits difference right there. 27 and 36, that's nine digits of difference right there. So the square root of 27 is going to be pretty far away from the square root of 36. And the square root of 27 is actually going to be pretty close to the square root of 25. So I'm going to estimate this to one decimal places as about 5.2. Again, really close to the 5, not quite 5 and pretty far away from the 6. I'm not going to guess 5.1. Maybe if it is the square root of 26, I would guess 5.1. I'm just going to go with 5.2 for now. That's a pretty good estimate of what that is. All right, the second one over here. Now notice here that I have a negative out front. Now you might think, oh, negatives and radicals, they don't mix, so that means I can't do this. Well, not necessarily. Negatives outside the radical are actually OK. It's when we have negatives on the inside of the radical, that's when they're not OK. We don't want to have negatives on the inside of the radical. Anyway, so square root of 32, or excuse me, the negative square root of 32, get rid of some of that. So my answer in the end is going to be negative. So let's just worry about the square root of 32 now. So again, kind of the same deal over here. 32 is in between 36 and is in between 25. So now I've got to decide to myself, is 32 going to be closer to 36 or 25? So is it going to be closer to five? Or is it going to be closer to six? Well, in this case, it's actually closer to six. It's only four digits away from here, but it is seven digits away from this one. So it's about halfway in between, not quite. It's actually a little bit closer to 36. So I'm going to guess this is going to be about 5.7. Not quite in between, but still closer to 36. That's about 5.7. Don't forget the negative, that's out front. So my estimate is about negative 5.7. OK, last but not least over here. Now we have kind of a different number, a little bit smaller. But notice here, we've got a negative underneath a radical. This is what we're going to say, no real solution. We cannot have a negative underneath a radical. I put that there as just a reminder of the difference between the negative outside the radical and the negative on the inside of the radical. So we cannot look at, we cannot have any real solutions for this type of problem. OK, so anyway, that is estimating square roots. That's just a very short video on how to do that. Hope this video was helpful.