in this unit we're gonna take a little break from our geometry and we're gonna work on some algebra skills to just help you keep fresh on those and remind you about those between algebra 1 and algebra 2 which is the next course you'll take there aren't going to be separate guided notes these videos will just go through and highlight actual homework problems for you so then you'll have a worked example for each one of your homework and then there are some more worked examples on the answer key and obviously you'll have your mastery quizzes to practice some more so we are gonna start with homework problem number 5 in your packets so if you can find that homework problem now radicals as a word sometimes mess kids up another synonym would be the square root that square root or as we worked in the similarity unit we talked about the cube root and then we put that index number of a 3 here that 2 for square root is written there but since it's the common one we don't write it just like we don't write a 1 in front of a variable but we know it's there the key to this chapter to urge this section is that squaring and square rooting are opposite operation cubing and cube rooting are opposite operations they undo each other so when we're looking to simplify we're looking to leave as exact answers we are gonna take out all of the perfect squares it's kind of like reducing a fraction we're gonna take out all of the perfect squares and we're gonna leave the non perfect squares underneath the radical so there's some shortcuts to this and if you know your perfect squares 1 squared is 1 2 squared is 4 3 squared is 9 4 squared is 16 5 squared is 25 on down I recommend learning them through 15 squared it makes your life a little easier because you'll recognize perfect squares when you're factoring and you can stop sooner if you don't it's fine you can factor it all the way down to prime factors and you'll get there so the first thing we're gonna do is we are gonna take and we are gonna factor 392 now 392 is an even number so I know that 2 goes into it and 2 will go into it 196 times if you know your math facts 196 is a perfect square if you don't we're gonna go ahead and say well it's still an even number so 2 goes into it 98 times and 2 goes into 98 49 times there's another perfect square or I know that 49 is 7 times 7 so I've factored that now I want to think about everything in terms of squares so I want to rewrite all of my factors in terms of squares so this 5 is gonna stay out here and I'm going to rewrite 392 in terms of these factors and I'm going to group them as perfect squares so two twos makes two squares there's a random I'll just leave that as a two and two sevens makes seven squared I'm going to do the same thing with these exponents on these variables X cubed is x squared times X there's still three of them Y squared is a perfect square Z to the fourth I'm going to write that as Z squared times Z squared so I haven't done any math except to factor and break everything down into perfect squares and these are the ones that I'm going to focus on so what's going to happen is I'm going to go through in this operation between this 5 and the radical is multiplication it's like a coefficient in front of a variable it's multiplication anything that comes out from underneath the radical gets multiplied so I'm have my five and I'm going to leave a blank and I'm going to have my radical so this I might look at each of these that so basically I'm going to say the square root of two squared that's this part right here well that's going to cancel and a two can come out I can do that operation but this two I can't take the square root so it stays under the radical the square root of seven squared is seven so that comes out the square root of x squared is X so that comes out but this X doesn't have a square root so it stays under square root of Y squared is y square root of Z squared is Z square root of Z squared is Z so then I just have to clean this all up all of this gets multiplied so I have seventy X Y Z squared this is my leftover and so that's what I leave as my exact answer I've taken all of the perfect squares out and I've left that as my exact answer