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okay hello we are going to continue and module 1 and now that we know about rational numbers want to talk about Roots what are Roots while before we talk about Roots we got to talk about something else and that is exponents so I think you probably know what exponents are but let's just make sure no wait you know what let's just take a break first let's do a little puzzle can you find the next numbers in this sequence 24860 I see the pattern here it's just doubling every time and then it's multiplying play to again and then it's multiplying by two again not too difficult but what you might not see is that in this sequence you start with to and then you multiply that by 2 and then you multiply that by 2 so that you got 2 x 2 x 2 and then you multiply that by 2 can you multiply that by two and if you kept on going you would eventually just have tons and tons of twos and that's all great and that's a nice and play pattern there but what I want to point out here is if you had 2 * 2 * 2 * 2 * 2 * 2 * 2 there's got to be an easy way to say that and write that and there is and we do it with exponents exponents a big long expression wear your multiplying the same thing times itself over and over and over again and abbreviates it shortens it into something shorter sweeter like 7 to the 6th power instead of 7 * 7 * 7 * 7 * 7 * 7  you can also call this 7 ^ 6 I think this is probably review but just in case you don't remember this six is the exponent with the seven which means you're going to multiply 7 * itself 6 times alright it means repeated multiplication  know that set 3 to the 4th power would be what it would be 3 * 3 * 3 * 3 and if you multiply that out you get 81 if you do 10 to the 3rd power repeat 10 times 10 times 10 which if you multiply that out comes out to a thousand and if you had 23 to the first Power I guess that's just 23 right yeah okay so what's 10 * 10 thats an easy one that's 10 to the second power attend to the power two or  we could also call this one 10 squared when it's the second power we call it 10 squared turn nickname and when it's the third power or ^ 3 we call it cubed these are special nicknames for an exponent to which is called squaring something and an exponent of 3 which is called huming something okay you probably already knew that too cuz you're so smart but  can you use an exponent to rewrite this  try it in your Journal and then once you're done with that try this one  take five to the fourth power and tell me what it comes out to and now that you know all about exponents we can do this little exercise 1 squared what does that well that's just one when's one which is one two squared is 2 times 2 which is for what's 7 squared 7 x 700 that's 49 and maybe you don't know what 12 12 is but it's 144 these are easy when you square a number the thing about this last one though is we're not squaring a hundred we're not going to do 100 * 100 we're trying to figure out what times itself makes a hundred and in order to figure out what that number is they should go in the blank spot you kind of have to unsquare the 100 don't you you have to try to go backwards in your my what time is it sound will I know 5 x 20 no that's not to * 1504 * 10 that's not too difficult but what you just basically did is unsquared the 100 because you needed a number times itself that made 100 and when you unsquare a number like that you just found what's called a square root okay so a square root is can you unsquare something and 10 is the square root of 100  the way we write this in math with a square root is with this kind of a funky little Sim that looks like this 10 is the square root with that crazy symbol of 100 and so if I said what are we trying to find here we're trying to find the square root of 25 so what time is itself makes 25 oh yeah 5 is the square 425  okay easy enough by the way that crazy symbol it's called a radical and a radical just means that your what's the square root of the number inside of the radical  so could you square root 64 it should be a try could you square root for should be too right  what about 81 oh yeah that's 9 x 9 square roots aren't that hard the square 249 is seven because seven times seven makes 49 and you Square the 49 into a 7 but what if you have three to the third power three cubes we know that's 3 * 3 * 3 which comes out to 27 when you multiply it but if we wanted to go backwards from the 27 to the three that got key if we want to. 27 what would we do would we use a square root no we couldn't use a square root because that would be on squaring it and we want to uncube so if you want to something you have to do a cube root a cube root is just like a square root but instead of fun squaring it you have to uncube it so we're not saying what turns itself makes 27 we're saying what times itself times itself makes 27 and since 27 is 3 x 3 x 3 the cube root of 27 is 3 cubed it so what about the cube 125 oh yeah yeah that's a tough one right what time is it self times itself makes 125 cube roots aren't always as easy as square roots what time is it helps to make a factor tree what I mean by factor tree is  can we break 125 down is it 5 x 25 check it on your calculator it is and then can we break the 25 down oh yeah 25 is 5 * 5 wait a second 125 5 x 5 x 5 there for the cube root of 125 is 5 and you can check it by doing 5 times 5 times 5 and seeing if it give do you 125 which it does so that's a cube root alright what about the cube root of 1000 will do this one quicker a thousand is 10 * 1 100 is 10 * 10 so isn't a thousand 10 x 10 x 10 sure it is there for the cube root of 1000 is because a thousand is 10 x 10 x 10 now it's your turn can you do this the square root of 9 and can you do this the cube root of 8 try them and see what you come up with when once you're done with that we need to talk about something else we just did the cube root of 8 hopefully you got it right we'll see you tomorrow but you can also do fourth roots and you can also do fifth Roots now the number eight doesn't really have a fourth root or a fifth root because nothing time to tell time stop * itself makes 8 but it is possible to do any kind of root you can unfit something or unfort some okay that number above the radical is called an index and if you want to pause this video and read this little paragraph you can but what it basically says you can do square roots or cube roots or fourth roots or fifth roots and that index tells you which kind of a root you're doing and if you're just square root of a number you don't have to write the little too because if there's no number there we just assume it's a square root  one more what if I asked you to solve this equation and tell me what x equals you would probably know pretty quickly that 60 men's 4 x 4 and therefore X must equal for right well kind of you're almost there because there's something else tricky about couldn't you make 16 by doing -4 * -4  wouldn't -4 Square to give you Christine so therefore does X just equal for no X could equal positive for or neg for and when use that little plus minus symbol to mean that X could be 4 or negative 4  tricky huh but it's true all right so try to tell me what does x equal if x squared is 100 and I'll you should use that little plus or minus symbol  okay that's it thanks for watching thanks for listening hopefully it took good note can if you have any questions write those things down in your notes and we will talk about it tomorrow

Uploaded by Jeff Marbut.

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