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Math Help - simplifying radicals following the four radical properties

  1. #1
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    simplifying radicals following the four radical properties

    i'm following paul's notes @ Pauls Online Notes : Algebra - Radicals and needless to say i'm starting to get a little confused.

    I'm on the example 3c
    simplifying radicals following the four radical properties-eq0047m.gif

    So because the radical is larger than the index, it must be simplied..got it. i understand that you have to break it down as well. says that we must break them up into perfect squares, which gets this.

    simplifying radicals following the four radical properties-eq0048m.gif

    Now i'm lost with this. How did the 18 get divided by two?
    i understand that the y must be cut as its a multiple of 2, by why did it turn into a 2y? to me it seems like it would of been a y10 y..instead of a y10 (2y). i seem a bit lost on where that 2y comes into play ..or how it came to be. any pointers?
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  2. #2
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    He's pulling the 2 out of the 18 and sticking it on the extra factor of y. Basically, it's the same as

     18x^6y^{11} = (9 * 2)x^6y^{10}y = (2)(9)(x^3)^2(y^5)^2(y)

    He's doing it because 9 is a perfect square (3*3), and he's trying to factor out all such squares. Make sense?
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  3. #3
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    so what if the 18 was a 20. would it still be divided by 2? or was the only reason it was even divided by 2 was because it took it to a perfect square. i'm sure you already said that, but i'm just making sure lol. but if it was a 20..then the x3 and y5 would not of been multiplied by 2?..
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  4. #4
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    No, because 10 isn't a perfect square. However, 4 is, and  20 = 4 * 5 ! The idea is to try and divide out a perfect square so that you can take it outside the radical.
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  5. #5
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    i think i understand a little. this may be a bit much to ask, but is it possible you could give me an example of this and let me work it out? lol
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  6. #6
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    Sure thing! Let's do something like...

     \sqrt{ 24x^5y^7}
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  7. #7
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    before i reply to that, can you tell me how to make symbols so i can stop looking gimp with my typing lol
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  8. #8
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    Sure. There's a latex help sub-forum that will go into more specifics, but in general, if you want a piece of writing to be in that style, begin by typing [tex] (text goes here) [ /math], without the space before the slash. If you double click on my writing, you can see the text that generates it. Use \sqrt{} for a square root, ^ for raising something to a power.
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  9. #9
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    Quote Originally Posted by Math Major View Post
    Sure. There's a latex help sub-forum that will go into more specifics, but in general, if you want a piece of writing to be in that style, begin by typing [tex] (text goes here) [ /math], without the space before the slash. If you double click on my writing, you can see the text that generates it. Use \sqrt{} for a square root, ^ for raising something to a power.
    k after looking at this it might go a little better for my learning if we go step by step. for some reason i want to take the 24 and divide by 3 to get an 8. also the x^5 i want to take down with a multiple of 2..so it would end up being x^2^(^2^) x^1 ?
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  10. #10
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    Sure, we can do this in steps. You are correct that

     x^5 = x^2 * x^2 * x .
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  11. #11
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    sorry i had to go on break at work

    was i wrong for dividing the 24 down to 8?
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  12. #12
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    You need to divide 24 by a perfect square. Try factoring it down and seeing if you can spot any.
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  13. #13
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    24/6 4..which is a perfect square
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  14. #14
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    Correct. You've factored x and 24. You just need to factor y and then take the perfect square out of the radical.
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  15. #15
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    Quote Originally Posted by Greysoul View Post
    24/6 4..which is a perfect square
    4x^2^(^2^) x y^2^(^3^)y

    i feel so amazingly lost. radicals went from easy to extremely mind boggling. i feel like i'm missing something, i keep thinking about that 2y from earlier..as if my x and y that are alone should have had something done to them
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