hey guys mr b here again bringing another video this is uh the third video in my radical series i'm making for my quarantine students and uh we are just entering quarantine here so um basically that means we're online for at least two weeks and then we'll see what happens so if you haven't watched the first couple videos in my uh series you might want to re consider doing that and basically what those videos are on are how to deal with the variables underneath square roots and the other one is cube roots so it's like one of the skills you need to be able to reduce radicals right so if you got variables you got to deal with them just like if you got a numbers we got to deal with them so i haven't made well i probably got one somewhere on my video of how to reduce square roots and um cube roots but i'll probably make another one of those as well and i'll just drop i'll drop the first two down in the description or i'll put a little card or something fancy um so let's go just jump right to the chase and let's do an example so i've got the exact same one on the front page there square root of 50 x and there's some some stuff left there from the last time i was working at this i can hear i can hear my class saying oh bye well yeah you don't have a clue what you're doing half the time is true but uh yeah so we've got square root of 50. so 50 is not a perfect square so if you don't remember that list of perfect squares you really need to so i'll just write it here on the side 1 4 of course one is useless to us 9 16 25 36 49 64. so it keeps going on this just 1 times 1 2 times 2 3 times 3 4 times 4 5 times 5. so anytime you want to get this you can just multiply the number by itself right so 50 is not on this list therefore we have to deal with it it's a pain also our rule for taking the square root of a variable x to the 7 is we check the exponent if it's divisible by two it's perfect seven is not therefore it is not perfect we gotta deal with it so when i'm first doing this a lot of times what i like to say to students is you know what you got two individual problems here you got root 50 and you got x to the seventh they're separate right you got to deal with them individually and it's a different you know it's it's a very similar technique but they're a little bit different right so root 50 i have to look on this list and see which one of these actually divides and usually i work this way on the list i start high and i go low so i want to find the highest perfect square that divides 50 so obviously 64 is not going to work it's bigger 49 is not going to work 36 is not going to work and bam i hit 25 so 25 is gonna work 25 divided into 50 equals two so i can break this guy up into a perfect square a number on the list 25 and then 2 right so square root of 50 is exactly the same as the square root of 25 times 2. so the thing about 25 is i know the square root of 25. it's 5. so i'll break this up into its two individual roots now the square of 25 like i just said is 5. and then i get left with that root 2 here behind so root 50 is the same as 5 root 2. all right so that's reduced we're good there's no perfect squares inside of this guy to take out so that guy's finished so now square root of x to the seven i gotta deal with this so remember our technique and if you don't remember drop down in the description watch my videos on square roots of ra of the variables so what i want to do is i want to drop i want to use the exact same technique i want to find a perfect square variable so my perfect square variables are the ones that have exponents that are divisible by 2. so we could make a list of this too right x squared x to the 4 x to the 6 x to the 8 and then they keep going every second number right every even number so i want to find the biggest one that's closest to x to the seven of course that's x to the sixth but all i ever need to do is drop it back one every time right so i take this exponent i break it up into uh six plus one which is seven so now i break it up into two individuals so x to the sixth and then x to the one now i don't need to put the one there so this the square root of x to the sixth well i need to do is divide that exponent by two just x to the three root x so now individually those problems you can probably do on your own well putting it together in one question is not that complicated you already got it done you just have to treat them individually now you don't necessarily have to need to write it like this but basically what that means is this guy turns into whatever's on the outside so the five and the x cubed they get multiplied together so 5 x cubed and then whatever's underneath the square root gets left and you end up with 2 x now in general i wouldn't write it like this i would just continue the problem down the page underneath the root at the same time so that's why i'm going to deal with the next one all right so actually i think i'll make up another example down here and then the next one i'm going to do a little differently so let's try b we'll call this a2 because i think i got to be on the next page a2 so let me make one off the top of my head so i'll keep it i'll keep it simple 12. x to the nine all right so certainly nothing simple about this stuff but you know in terms of the scale of these questions this one's a pretty simple one so i need to find a perfect square that divides into 12. so that number is 4 right so i work backwards and the number that divides into 12 is 4. so i'm going to break 12 up into 4 times 3. so you see how i'm going to write this one a little bit different i'm going to keep it all underneath the root this time but again if that method up top works for you do it every single time now x to the nine so we got that's not perfect not divisible by two the exponent so what i need to do is i need to walk it back one so x to the eighth that's perfect square right there divisible by two and then x to the one so what i end up with when i have this situation is i have perfect not perfect perfect not perfect so anything that's perfect i group it up so i might go four x to the eighth so that's my perfect stuff and then my non-perfect stuff well it's just 3x so as we know the stuff that's perfect i'm taking that out i'm going to actually compute it right i'm going to evaluate it take the square root of 4 take the square root of x to the 8. well 3x i can't there's literally nothing i can do with that right so so the square root of 4 is 2 that's on the outside of the root square root of x to the 8 well divide 8 by 2 is 4 so is x to the 4. and then this guy right here root 3x goes right here it's left you can't do anything with it you keep it alone so there it is i reduced down from here all the way to here now i can understand this way is a lot more complicated in terms of well it's a lot more complicated looking it's basically the exact same thing as what we just did up up top so um you know whatever way you want that's the way that's best for you right i don't really care whatever way works for you get it done and there's steps that you can skip some people can get from here here without um doing some people can get from here all the way to the last step so whatever works for you i'm just interested that you understand the process and making sure that you can do it all right let's try another one so this one's going to have two variables in it and again that doesn't change anything we still got the exact same process we got to deal with each thing individually so i got to deal with the 45 i get a deal with the x to the 12 and then i got to deal with the y to the 17 through each individual we have their three processes happening so 45 again on that list of numbers we got to go down through so flashback for a second so 45 doesn't work with any of these until i get to 9. and literally i've been putting my calculator if i didn't know 45 divided by 25 even though you should know that's not going to work you got to try if you don't so 9 is the first one that work and 45 is 9 times 5. so number on the list number not on the list x to the 12 that's already perfect right x to the 12 12 is divisible by 2. nothing i have to do with that guy it's good to go i'm dumping that in the next step and then y to the 17 not perfect 17 is not divisible by 2. so i end up with y to the sixteen so i gotta break it up right i gotta break it up into a perfect square well the next closest one to seventeen is y to the sixteen and then y to the one right so all has to happen for a variable is for the exponent to be divisible by two man i'd be rich if i got a dollar for every time i said that this morning so now all the perfect stuff goes together the 9 x to the 12 y is 16. so uh 9 x to the 12 y is 16. those are best bodies all perfect and then 5 and the y those are the misfits they get left behind okay they're not going anywhere so these are non-perfect so that means they have the left behind underneath the root square root of nine that's three square root of x to the twelve i divide the exponent by two it's x to the 6th and then uh y to the 16 well divide the exponent by 2 becomes y to the 8th so those are all the perfect um squares and then now i'm left with 5y left behind all right this video is getting a bit long guys i plan to address cube roots in this but i think i'll do a separate video for that again thanks for watching i know it's tough times for a lot of you guys trying to learn online by yourself but you know what uh there's a lot of good teachers out there making a lot of doing a lot of good things so make sure that you take advantage of all the creators on youtube and all these stuff that's out there thanks for watching guys i appreciate the video i appreciate the all the hard work you guys are putting in and i'll hopefully see everyone soon thanks for watching