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Hattie Kilgore
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Simplifying Radicals (with indices other than 2)
Added Apr 03, 2020
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hi folks it's mrs. Kilgore and I'll Sprint Annie welcome you need to learn in Life or how to pursue first of all Let me give a shout out to my husband for my artwork we thought maybe you needed smile and a chuckle so hopefully it's brought a smile to your face today and I'm going to be doing I'm going to try to do a lesson for each new assignment that I give you since we are getting into new material but you may or may not have one every day because sometimes it takes a little while for them to upload and and sometimes technology you know how that is cheap checking your Schoology I get everything that comes up I want to talk today about some radicals we talked about them a little bit but we want to go a little bit farther today we're going to do maybe a fourth root or if it's root word they can talk about can we take a an even root of a negative number and things like that and just do a little detail thing and also do a few problems and what I tried to do to go to your cell exercises that I'm giving you and I've tried to Taylor some of my examples and some of my practice to the types of questions that you're going to sit but remember there are some Clues there's some person examples on each question so if you need to go to those go to the okay but if you need me please please contact me by email and we'll see what we can do if necessary reach out to reach out to a buddy FaceTime Hummer ride from a question and see see what they think's going on a remember I want you to get these at 2 smart score of 85 Place receive credit for them all right cuz we are going to start today then with just a couple of days stick problems and if I asked you for insta what is the square root of 49 Kennywood sell mini I certainly hope hey and it's sad because 7 x 7 is 49 now one of the questions I want to ask you on your diet fail is first of all was going to ask you to simplify √ 49 we always do give the positive portion of that okay babe I ask you a question how many real roots does 49/2 for the square root of 49 if you are taking and even rude if it's a square 4326 straight whatever you actually have two real Roots K and the other one would be -7 and it would be -7 as well because -7 squared if we square a negative 7 negative 7 negative 7 is also that 49 no case of there might be some questions play if we haven't even root how many real Roots do we have well we're going to have to cuz we're going to have the positive or we are going to have the negative is that okay simplify what is the √ 49 is just the flying owl 7 if the positive is what what they're asking for their OK Google what is it what's the square root of -49 we've already done that remember Anna square root of a negative or an even index of a negative number we can't do it that's going to get offended as imaginary numbers and for the exercise that you're going to do you are doing real answers okay now having said that let me go ahead and look at this what if I asked you for say the kitty Brew of a -27 banana can you for the key Brave I'm asking you for what times itself 3 times will give you a negative 27 well if you're taking an odd root of a negative that's perfectly acceptable you're just going to get a naked okay so yes we certainly can take an odd root of a negative matter we will not get an imaginary will do so the cube root of a negative 27 is -3 because -3 * -3 * -3 is -26 so it's okay to take an odd root of a negative number and of course we are just going to get one real root for that okay alright I know you can't answer me but I'm in that habit so I'm going to continue to ask that question okay so if you're going to answer hey there are two real rich graph to simplify just give the positive portion of it if the index is odd there's one real ripped okay and yeah if the index is needs to be positive to get real rude and then if the end is odd the radicand can be or maybe let's play like that radicand may be positive or negative when I say radicand what I mean folks is the number or the variable underneath the radical symbol for the radicand being would be if I did the cube root of a negative 27 then the radicand would be the negative 27 the index is great we're taking out here okay so the three would be in it and then the radicand is a -20 is that okay does that make sense all right then see you're going to I was to you that you're going to have to simplify and you may have to take the the root of a number you may even have to take a particular root of a fraction that is a couple is that okay alright so let's say we had and you can use your your calculator here folks are going to be perfect roof and you'll be able to take him in your calculator that's fine remember your calculator is a tool and you may certainly use it okay to just a couple more problems here let's say we had we'll just call this practice let's try that way add 3/8 of 32 and then we had the fourth root of 81 hey now the fifth root of 32 I'm just looking for something that will multiply by itself 5 * 2 give me 32 and I believe that's going to be too and that may not be right on the top of your head that that's okay you're perfect I want with an ex would be 81 * 3 with the 243 would be your next if perfect fifth number three to the Sephora Keizer that helps you keep you a little list of those handy but keep your calculator handy as well okay then the fourth root of 81 I believe is 3 because 3 * 3 * 3 * 3 is 81 okay then what do a couple here where we have to do maybe a root of a fraction so let's do the √ 16 ever I do want I know none of us are really funny and really thrilled with fractions so let's go ahead and take the square root of all we can what's the √ 16 that's going to give us at 4 what's the square root of I do want that's going to give us a 9 now we went over the other day what if that 81 was perfect square we went through what we have to do to rationalize that denominator so we might have to do that and it's the same process if you were to run into some idiots kiibru he would Ghost Rider denominator mouth whatever would make it a perfect Cube so if you need some more help with that let me know okay and let's do one more here how about that you've read -20 steps / 125 now the question here is can you take the cube root of a negative absolutely you couldn't take the Asian right you can take a square root of a negative 27 / 125 and get a real rude and remember right now we're looking for Real Rittz that we can take this rig so what's the cube root of a negative funny sad ride is a -3 + what is the cube root of a 125 I think you're going to find that to be a 5k do we end up the cube root of -27 over 125 is going to give you a negative 3/5 hey do I have any question site okay then I think that'll get you through the first couple of assignments on the air now I'd like for us to look at conveyor belt and we've got a few things. To do with you and I've got one little thing that we need to be careful with and I'm going to go ahead and just show you sort of a ride up of that and then we'll do some examples with it right this to get you through the next two assignments I hope okay let's just read through the second and we'll talk about what in the world is she talking about okay all right so when working with variables we must be careful to get a positive answer outside the rat when working with Ethan and the city first of all these is just plural for index so I'm talking about the route that I'm taking k talkin about a square root or 4th graders fixed-route or whatever we have to be careful with that because remember were talking about real rude and if we have a variable underneath the ride call if it's a variable we don't know if it's representing a positive or A negative but if we can take the root of it we need to take the positive portion of it because that's what we're actually or we're looking for a real red so therefore we will use absolute value if working with the Seas we do now I have to worry because we can find an odd root of a negative number it will just give us a k let me tell you an example of what I'm talking about here and I'm going to say simply use this problem right here to get us started here and then we've got a couple more to look at so let's start with this one and weave the square root so we've definitely got an even and Dad at 1024 at today positive there is exactly what we wanted so we got the square root of 1024 and we are going to get we want the positive portion of that so I'm just going to double-check here and I believe I know what that is but I'm going to double-check myself and I believe the square root of 1024 is just a 9:30 2K I want the positive portion there so I'm just going to write that it's 32 and I'll have to do a whole lot to it calculator did most of my work I know that call Sister Dee still got it written down and yes there are but if it is understood that we want to ride down the positive port song after worry about the absolute value with C with the S Pen we don't have to put we don't have to just automatically say hey if there's even we got a stick at flute value around everything okay so for instance what is the square root of x to the 10th power remember what I told you about that if you're dealing with a text if your exponent is divisible by that and debt just divide it says 10 / 2 is 5 that's going to give us at today hey now let's think about this just a second if X4 say -1 if I raise a -1 to the 10th power I get a positive one when I come out here and I'm taking the square root of it is -1 to the 5th is -1 * Stanley change this out the negative and I want to ensure that it's positive okay so when I take the route if I'm dealing with an even in debt can I take the root of that number if I get in X-Men around here then I need to put absolute value around it okay the 32 taken care of I don't have to deal with it but I do have to deal with this at 2 V because I want to make sure whatever it was that when it was raised to the 5th power it will come out as a positive and that absolute value does that for me head and you're going to have a few questions on your I say over you may have to make some decisions about that absolute value okay right is everybody with me any question hey let me show you something else here last night at we had the square root F-100 accident let's take a look at that now what's the square root of 100 going to be at 10 what's the square root of it to the A latest divisible by a square root so 8/2 it's 4 I'm at to the for now look at the difference here this time I've got my it's raised to an even exponent so if I've had a negative one over here for apps with say let's give an example their negative a positive one where can I buy -1 to the X to the fourth if we write -1 to the 4th that's still a positive isn't it negative 1 times negative 1 times negative -1 so it's going to take care of his fail if we end up with an even here folks we're okay we don't have to ensure the absolute value around to make it pop so if you happen to take the absolute value are teeth and parting if you happen to take the even root and you end up with an even exponent you don't have to work about the absolute value but if you take an even Ruth end up with an odd exponent that's when you need to worry about the absolute value that makes sense okay now let me give you one where you don't have to worry about the absolute value here as well how to make if you want more little situation here left side since you had the fifth root of negative at 2 V Y tu V first of all you may be concerned about that little negative right now well that's okay we can take an odd root of a negative and remember that's just too negative one has awakened types of its root of a negative one and then I think it's going to be pretty easy to take the fifth root of x to the phia and text it to you through what times itself 5 times give us a negative one I know you're telling me it's a negative once I'm going to go ahead and write that down you could just put the negative if you wanted to you wouldn't have to put the one with it okay how about this braided at 2 V ye we've got a NetSpend in here this to do bubble by 5 so V shred of it just divide 5 by 5 that gives a text to the first Jack what's the death rate of Y to V add just a wide to the first or why there you go okay I've got all that stuff NFC or do I need absolute value no and you don't need to worry about absolute value because you have an odd index does the end mr. As we stayed up here it's his makes any sense to you if working was odd and the Seas we do not have to worry hey to just give us a negative answer and it doesn't matter what and why I started out it okay alright so I have any questions to that point okay let's do just a couple of other little situations here will call them with some very maybe where we have to do just a little bit of simplification before we can deal with us so we'll do that and then I'm about through and you can get started on your assignment okay change job screens here just to say so we're going to do a little practice and this is some of those where we might have to do a little simplification before we really get to it okay so I'm trying to listen let's do the Sims free will start with an odd index the time assertive teasing of -32 Etsy the situation kind of what we're okay alright first of all is it okay to take an otter what is a negative net definitely so we're not have to worry about that we're just going to get a naked can I take the fifth root of an x to the 6th 6 cancel my 5 is it thundering to need to rewrite some here so let's go ahead then and let's rewrite this at the fifth root -32 X Sia contact to the first remember how we did that and now we'll take the fifth root of what we can K I know if you were here in the classroom or here in my dining he was play the fifth grade of a -32 is -2 and yes your calculator will do that so because it's an odd index it will take an odd index of a negative never what's the 5th grader next to the Sia well 5 is divisible by 5 isn't it so we've got it where we want it to the fifth root of x to the field is X today first or just add and remember it's it's fine I'm just putting the one there as extra emphasis now can I take the fifth root of x to the first I can't do it so what I will do then is I will keep my radical make sure that you put your index in there my doesn't look so good but that's supposed to be at 5 and then IRA and Ernie if we did if it was square root the other day once you're at stomach get smaller than your index then you've gone as far as you can go okay but we've simplified this in Jeannette on the fifth root of x hey do we have any questions like okay let's try another one here then how about lychee bread have it to the 13th why did they burp now I forgot to ask one question up here I'll never one was there any need for any absolute value no there wasn't because it was an odd ended to begin with remember we only have two sorry about that absolute value even and it to begin with that are never too are we going to have to worry about absolute value now we are we are however going to have to read re-rock you're just a little bit cuz that's the desert saying 13 is not divisible by 3 is it so let's go ahead and rewrite that and I think I'm going to try at the 12 Con Air and then why Cube should be good because three is divisible by 3 that hey what's the cube root of 8 to the 12th rat that's going to be at to the fourth 12/3 is 4 can we take the cube root of x to the first know once the exponent gets lower than or less than where is Ray Lewis III at so we got the key root of that and how about the cube root of Y Cube cube root of like you'd is why because 3/3 is 1 you can put the ones in there if you wish and we end up with that to the fourth y to the first times the cube root of I remember you require this time because we had an odd and that to begin with okay alright any questions okay then let's change gears here just a little bit and well let's let's do more I found this this to me and cuz you could stay there now some of you might look at that tan it's because you're thinking oh God x + 5 in parentheses why did you put that in there and I'll get together there all right let's put think this out here we got an audience I've got a negative in there can I take a note absolutely am I going to have to worry about absolute value go ahead and get it and a negative so good what's the cube root of x + 5 the cube / the three here 3/3 you can put the if you want there's really no need to multiply it out there okay all right any question okay Seymour little problems here then and then I'm going to let you go for this last time okay so for this lens let's do a square root remember I'm not really going to sit at 2 today or you can but generally you don't see that you got it to the a z to the 12th write square root of x y to the A leads to the Twix hey let's let's look at our situation here hey I have to pay for an even index am I going to have to worry about absolute value or at least be concerned about at sleeping yes I am is everything written such that I can take the square root of it absolutely because I've got all hear ye cable is still with what we've got we're going to divide each one of those exponents by 2 because that's very hectic / 2 is going today at Cinebarre 8 / 2 is going to be Y for the 4th and 12 / 2 is going to be 4z to the sticks I did that didn't think so bad did it but I've got to deal here just a little bit and I've got to think about do I need any absolute value remember because it's an even and debt I want to assure that my answer is positive my trick here that I used for the better word is if I'm taking it that and I end up with an odd exponent like the excuse here I cannot assure would be a toddler cuz I don't know what it was to begin with I don't know but there was a positive or A negative stuff I'm going to have to put absolute value around it to the third do it around watch the fourth and sea to the Sea no I don't because when I raise something to an even exponent it will give me a positive always so the only one that I need the absolute value around is it to the third if one of these others had been an audit you would have just put the absolute value around both of us to get okay but we are through now with that problem okay your question anything at all okay I've got one more that I'm going to do here with you but before I do that last problem with you I have a challenge here for you and I'm going to ask you she testified something for me and I would like for you to work it out on a piece of paper show me your stats give me a final answer take a picture of it and email me your work and your answer and whoever returns it to me first and it must be correct send your prize in the mail all right so here's your your challenge problem your bonus problem to see if you're paying attention and if you're if you're watching your your videos to help you out the I would like for you to simplify please √ 32x to the 5th why did the AIDS Dade City 18th just a little prize I'll mail it to you for whoever will work that out for me show me the set give me the correct answer app store values in all if necessary and send it to me by email the first correct answer that I get then I'll send you a price alright let's do one more little problem here and that is going to be number five and I think I can get it down here at the bottom we are going to do the 4th root 16x to the 10th why so the 12 Dade City 20th okay couple of questions yeah I think I've got enough friends not we'll just we'll go to another pay okay first off I've got a news an index town, so do I need to consider a possibility of absolute bad definitely hey I do have an even 6 or skis me a positive 16 there so yes I can take the fourth root of this one and get real roots what station is Siri. Well back to the camp Tim's not divisible by 4 is it thick chain has 1/4 radiant 12 is divisible by 4 by 4 tree right just a little bit here before we finish up let's do the fourth root of 16 and let's rewrite it to the tenth as it's to the eight find x squared that will get me an exponent less than my in debt so I'm good there and then 8 is divisible by 4 and then I'm going to eat my wife to the 12 and keep my Visa D20 hey they were ready with me to that hey now let's see if we can simplify that hey what's the fourth root of 16 what times itself 4 times will give you 6% I know you said to what's the fourth root of it to the a what times itself four times will give you access to the a Justified at 8 before that'll give you an x squared hey can I take the fourth root of x squared can't do it Canna so I'm going to put it over here in the radical and it you have to stay there I left myself a little bit of room because I still got the fourth root of a couple of things to take it what's the fourth root of life 12 / where is Surrey the desk in a Big Y to the Third because here on room and then what's the fourth root is z to the 20th 20 is divisible by 4 so the four free Tuesday 2 20th is day today okay and you may be looking at it and thinking happened but it is a simplified melt if you will hey Dad at their simplified version now one last question we said it was an even index and even route we were taking so we may need some absolute value where is our absolute value need it the rule is if we're taking and even in debt and we end up with an odd exponent then that's when we met absolute value on price does the x square need an absolute value no does my wife Cube Z to V need absolute value because I can't actually guarantee that that I don't know what why is so why were negative over here it would have made it there but then a negative here would negative to the third power okay so I've got to think about it's my indexes he's in and I end up with an odd exponent I need actually okay alright okay great keep working hard watch your videos remember your talents here for prize whoever gets his first to me by now with your war and correct alright you all have a good day keep working hard and let me know if you need me by email but I
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