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Hattie Kilgore
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Simplifying Radicals
Added Apr 03, 2020
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hi everyone welcome to learning live with geometry Gene we are going to go ahead and continue with our our standards and we'll get them RGA which is all about rocks and to deal with we're going to be dealing with us we may run into some answers simplifying a question casting practice on is sale on a couple of things on there will be too saturated theorem and it's Converse so let's go ahead and get started here we're sort of learning if we go with the document camera so be patient with me please the first thing that I want you to do here though is they go ahead and Raichu down from perfect square numbers and I have these listed in their classroom to remember on the board and these are yours to use it anytime this is only but you need to do what makes you the most comfortable and I know some of you are going to look at this and say I remember this from Algebra I did a factor tree and I simplify that way that's super if he like that and certainly use that but I'm going to show you a process here that sometimes I think it's a little little shorter and it's my preference but that doesn't mean it has to be your preference where does look at our first 20 perfect squares here and we are going to start with 1 + 4 + 9 + 16 25 + 36 + 49 64 + 81 and one hand navigate us to the first 10 and all I did there with the type 1 and squared + 2 squared it I got for 3 squared + 64 squared * 4 I found it the first 20 or so here will do what she needs to do for most of the time then we got 120 and then we've got 144 hanging 169 will be 13 squared + 196 and then say 25 is our 15 squared and then we go to 15 squared is 256 and 17 squared is 208 and 18 squared is 324 19 squared is 361 km + 20 sqrt is 4 I will tell you the first 10 are going to be the most helpful to us but I like to go ahead and it says first 20 cuz you never know be helpful today what we're going to do with it as long as it's in perfect squares and if I simply asked you for what the square root of 100 was and that she would tell me the square root of 100 a customer looking for √ 4 to give you that number underneath the radical there the radical is just the √ 100 / when there's not a number inside that little rascals. Names so if we went ahead and asked you for the square root of 116 we have no problem if we have that maybe the square root of 12 inside the square root of 9 or the square root of 16 answers where are they give us Death monster that give us familiar to us if you will now some of your square root of 12 on a calculator and I will get free point constant hair system that square root of 12 and in some cases an approximation is okay but the √ 12 is not going to be a Terminator it's not even going to have to make some decision about where we go ahead and that we really don't want to do hey unless it's specifically asked for more often we want to do what we call. So if you see simplifies for your instructions for if your instruction play leave your answer in simplified radical form what we're getting ready 30 square root of 12 is an example and we'll do that pray for others Harrison example, like we would do in class if I have to √ 12 I know that 12 can be written different ways you can say that's absolutely you might say I know that's correct it's also Sports Siri and I tell you what is 4 * 3 because I know that if I choose 4 * 3 the four is up here in my list of perfect square numbers and if I have a factor that's a perfect square and I can take the square root of that natural chews 4 * 3 - 2 use your calculator on this message has several members and that's okay today Service First Hat on Dish rewriting the √ 12 I'm just rewriting it at the √ 4 * 3 and then I'm going to take it apart I'm going to take the square root of the parts that I can play square root of 4 take the square root of story list of here the rewriting 3 and 3 * 1 it's not going to help anybody there so I'm going to go ahead and just called on the square root of 3 and that is actually simplified version of the square 12 their answers when were asked to simplify or leave their answer in simplified radical form India just a minute to let that I Canna think about that I'm going to give you a couple others here that we're going to let's practice am here together play the first one that we had the square root of 84 if you look up here in earlier I don't think you're going to find out on that list the closest is going to be 81 so I'm going to be working for all of my numbers left 84 sign and I'm going to hope that there is a perfect square up there that will divide into 84 so that I can rewrite it now sometimes you're going to find that there may be more that one perfect square that will divide in if there's more than one your best option is to take the largest number it will save you a lot of steps in a lot of effort and a lot of time under their skin how to jump-start I hope you've already and I think I have found that the perfect square that's going to divide into 84 and 4 * 21 and then I'm going to take the square root of what I can so what's the √ 4 Take It Outside the radical square root 21 layout let's think about √ 21 for just a moment 21 and 3 * 7 is also 1 * 21 either of those are any of those factors perfect squares they're not are they so can I do I really can't hear I'm not even going to spray tan said it but it's really not necessary so I'm always at the end at the √ 1/8 + √ 80 has been simplified to 2 on the square root of 21 and I'm through with simplifying that particular radical hey let's continue a still a couple more practice here and we're going to do the √ 98 now if you look at that the first thing that you notice Maybe that's an even number that's a good way to look at it and that may or may not take you to where you need to go but at least to start so if you look at my nails perfect or maybe he looked at it and said he probably is just two times or not and when we look at Davis square root of a perfect square that are now it's not going to simplify that anything 72 * 1 is so let's leave it under the radical so is that √ 49 + √ 49 when is just say it and we will take it that we can do with that normally ask are there any questions but remember you can stop this recording at any time and go back and look at it and if you need to email let me know and we'll see what we can do it I would continue with another one what time we're going to have the square root of 80 but that's what can happen here is some of your going to look at it and say a lot C something is perfect a perfect square and I'm going to cheese Diaz list of also can't work I want to say hey I know that 80 is 4 * 22 √ 4 * 20 super 4 is a perfect square that looks good so if we did we've got the square readers take it out 20th where we're going to leave it on the inside because it's not a perfect square if we take this we can break it down at 4 and then we can take the square root of what's playing at what's the √ 4 that's going to be outside that's already there and then can we do absolutely not it's a prime number is going to have to stick under the radical and stay there so what we do yes we've got three times on the square MSR simplified version now there's another way to do this remember I said that we tripped give me the number that's a perfect square that will divide into it if we can find the just park at Square will save yourself some time and efforts to the other side of the old or how about the square root of 80 I think the team will divide into 81 it so we're going to get the √ 16 * 5 and I'm going to take the square root of what we can so what's the √ 16 + 4 and then we got to get the square root of 5 if I can pick the largest purple it's going to save me a lot of time and effort okay and then we're going to do just a teeny Twist on it and then we'll we'll finish up with some medicine fractions and some possible variables here in just a few Nyan let's try the square root of 204 I'm looking up a list of perfect squares and 240 is not there I look at a little bit farther and I think we'll visible back to believe that was also going to be divisible by 4 it might even be divisible by something even larger here then I'm going to start with my sore when I have to do an order here as well let's go ahead and start with with a known quantity to know what's 4 * 60 you all check my multiplication Southwest United sometimes my calculations I got to check my calculations and if I do something wrong you gotta let me know square root of 4 how much is square root of 60 not a perfect square 8 square rooted 60 out the other and in my thinking I'm thinking that maybe a 60 is a. Of 4 * 15 be able here again to do √ 4 * √ 4 I guess that's two times too and then can I do anything to it so I end up seeing with 3 * 2 square root of 15 equals 4 on the Square radar look what I could have done in some of your ahead of me here and I'm sure you're Google sandwiches and I believe that 240 is 16 * 15 I believe and I'm just going to die except that it's true yes so I said the square thing and then love simplification square root 64 + √ 15 is left for me as well but remember we don't know how to say the same thing at the same time either one of those would have work sometimes we got into a little extra effort into it and that's okay now we could also start with something like this or end up with something like this where we have so we can read this as 5 * √ 120 or 5 on the square root of 155 square root of 120 square root of 1 it's probably going to have some simplification here so we're going to look at 1 other ride here so I believe we'll get 5 * √ 4 * 30 and then we're going to take square root of what we can so what's the square root of 4 what's the square root of 30 square there's not a perfect square that so I'm going to leave it's at 5 p.m. on the square root of 30 I got to try one more of those just in case you see one and we are going to have kids square root of 200 this time it time to Square Register if we look at this plan that's a perfect square so tell me do not look at it and say hey 800 that's a perfect square so others have you Montclair school with us straight to 100 100 * 2 and it will take the square root of what we can square root of 100 is 10 and we end up with stick time and then we can't do anything with the square Reddit it so we're going to wear radar are there any question now you can answer back to me that I'm used to asking are there any question that you let me know if there are bye bye email yeah I'm going to end this way we're going to do a little bit more with different I know you all are working hard place can I need to do that let me know if I can help Danny and you all have a good day
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