hi guys I'm hoping all of you guys are doing okay but today what we're gonna look at is we're going to spend a little bit of time thinking notes on section 6.2 and then once you guys are done with that you guys are gonna be able to complete homework on this I just want to make sure that all of you guys can take notes and then follow along so all of you guys already have the note packet for this chapter so just make sure you guys follow along take notes and then hopefully you know you guys gonna be able to get your homework done as well today so in six point two we are going to concentrate on multiplying and dividing radicals so we're just gonna kind of continue on what we did in section 6.1 most of you guys should be in pretty good shape with this because you've done a lot of this stuff in the past but we are still going kind of spent a little bit of time on it just to make sure that all of you guys are clear on what you have to do so what we're gonna look at is we're gonna look at number one now there's two different ways you can do this okay you can take a square root of four which will give you two you can take a square root of 25 which is five and you just multiply these two times five is ten option number two is you can multiply four times 25 which will give you 100 and then you can take a square root of that and that would give you ten so when you're doing your homework you decide how you want to do it I think a lot of you guys will prefer multiplying all of this first and then simplifying it I think it will be a lot easier for you but you decide now number five I ended up doing these separately site that eighteen separate and I did 50 separate if you want to multiply them you can but for number eighteen because this is not a perfect square you do have to make a factor tree so you're gonna take it divided by two you get nine and then from ninety to three and three so because I have one pair of threes three is gonna come out and then the two is left without the pair's so that's gonna stay underneath the radical same rule applies for square root of 50 I'm going to take / - I'm gonna get 25 and then I'm gonna get 5 and 5 so I got 1 pairs of 5 so 5 is gonna come out and once again 2 doesn't have a pair so it's gonna stay underneath the radical you do still have to simplify this so what you're gonna do is you're gonna multiply 3 times 5 which will give you 15 and then square root of 2 times square root of 2 is going to give you square root of 4 but remember you can still simplify square root of 4 which is 2 so 15 times 2 is going to give you 30 many of you guys what you can do with this is you can actually plug this into your calculator your calculator can do that for you if you're gonna be able to get a nice whole number your calculator will just tell you that it's 30 now if your calculator is gonna give you an answer as a decimal then obviously you need to make sure you make the factor trees now continuing on we're going to look at the bottom portion of this now in the bottom portion of this we are doing the same thing the only difference is that we are dealing with variables and also we're dealing with different index so for number 8 we are required to take a cubic root of all of these things underneath the radical so in order to do that you're gonna type it into your calculator cubic cubic root of 125 which will give you 5 now Y Square and this is 3 well we cannot fit at 3 into a 2 so Y square is going to stay underneath the radical and then Z to the 4th we can make one pair of threes from that so the onesies gonna come out and then one of the Z's is going to stay underneath the radical but remember you do have to write this index of 3 in here otherwise you are going to be marked wrong on your homework so be very careful now for the next example number 11 if you notice there is no index in here that's why I ended up writing 2 in here so if there's nothing in here there's always a - so how many two of two's you can fit into a 2/1 how many we can fit into a 10-5 so that's how he got wise to the fifth now zzzz by itself it's like a Z to the first we can't really fit it to into a Z so therefore Z is gonna stay underneath the radical now notice that I'm not writing index of two in here because I really don't have to okay because it's already given to you that this is always a two for number 12 you are doing a cute fourth root of 256 so fourth root of 256 is four then you got to ask yourself how many 4s we can fit into a seven well only one and there will be three they're gonna stay underneath the radical and then twelve well T to the 12 we can fit three groups of four into 12 so that's how he got T to the third now remember because of that index being a foreign here you need to make sure you do write that in for your index number 13 we're gonna do the same thing you're gonna take cubic root of 216 which will give you 6 and then you're asked yourself how many threes can fit into a 4 well only one and then one X is gonna stay underneath the radical then you're gonna ask yourself well how many threes can fit into Y to the third well one of them so that's why we get Y on the outside once again X is gonna be underneath the radical and yes make sure you still write this index because the only time you don't have to write this index if it's a 2 so this all of this stuff is dealing with pretty much simplifying radicals what you guys did in 6.1 the only differences they do have a different index if you guys go on to the next page in our notes we're going to keep working on a few more examples just practicing on and they're gonna get a little bit more difficult but most of you guys should be ok with this you shouldn't have any issues with us so if you take a look at number 19 it's the same idea you are going to multiply 4 times 3 which will give you 12 and then you're gonna multiply 2x times 8x which will give you 16x squared now remember that's gonna be underneath the radical now you already know that square root of 16 is 4 and you know that y you can fit one pair of two's into X square so that's how we get 4 X the only thing left for you to do is multiply it so 12 times 4x is 48 X and then you're done for number 21 you are going to multiply 9 times 3 which will give you 27 and when you multiply square root of 2 times square root of Y you're just gonna get radical 2y now there is really nothing we can do with this example this is your final answer you're done now for 22 we're gonna multiply 12 times 3 which will give you 36 and then you're gonna add these exponents so 2 plus 1 is 3 and then for the Y 1 plus 4 is 5 remember if the variable is by itself there's always imaginary 1 in there so now you are going to simplify this so square root of 36 is 6 then how many twos can fit into a 3 one of them and one needs to stay under because it's leftover and then how many 2 so you can fit into a 5 you can fit two pairs of twos and then one will stay underneath the radical and that would be your final answer for number 24 it's the same idea as number 22 you're going through the same exact steps so you can just follow along these steps right here and then you can attempt doing that on your by your own and see if you're gonna get the same results now scrolling to the bottom the last thing that we have to go over with you guys is dividing radicals so with dividing radicals there's few rules that we have to follow as well so we want to make sure that all of you guys are going to do okay on this so whenever you're dividing the easiest way to do this is whenever we give you an example something like number 26 always just do two things make sure you divide your numbers and with the variables you are subtracting them okay and that is going to guarantee you to get the right answers so if you take 63 and divided by seven that is gonna give you 9x is there so X is going to stay and then you have y to the third and then you have a Y so you are going to subtract these so you get Y squared now the last step is to simplify so when you simplify this you're gonna take square root of 9 is 3 now how many pairs of two you can fit into a two well it's one pair so it's a Y and then X is by itself so that's going to stay underneath the radical for number 27 is the same exact idea you're going to take your numbers and the vitam so 54 divided by 2 is 27 then you're gonna subtract the exponents so 5 minus 2 is 3 and then 3 minus 1 is 2 now because 27 is not a perfect square you will be required to make a lo factor tree for 27 so you're gonna divide it by 3 will give you 9 and then you're gonna get 3 and 3 so you're gonna get one pair of threes so from that pair of threes 3 is gonna come out and then 3 that's left without the pair is gonna stay underneath the radical now how many twos we can fit into a 3 one of them and one of them is gonna stay under and then 4y square you can fit one pair of twos so that's why we got Y on the outside so as far as doing these examples Justin please make sure you do it exactly the same way and then you're going to do just fine now the last thing that I want to talk to you guys about for a minute or so is something called rationalizing the denominator so remember that in geometry your teachers have been telling you that you cannot have a square root underneath the radical so in order to get rid of this square root you're going to multiply the top and the bottom of your fraction by your denominator in this case square root of 5 so when you do that you're just gonna multiply these across so we're gonna get square root of 5y and on the bottom you're gonna get square root of 25 now we can't do anything with this so this is going to stay and then square root of 25 is just 5 now some of you guys might think like well I can take 5 and divide it by 5 we cannot do that ok this is a radical this is just a number the only time you can divide them is only if they're both have a square root just like we did in the problems above it you're gonna probably see only one or two of these on your homework because SAT doesn't really require you guys to rationalize the denominators so we are done with section 6.2 um just make sure you guys definitely take notes on this and then I'm going to be sharing homework with you as well if you have any other questions please let me know and then I will be in touch with you soon thanks bye