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

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.

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?

2. 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?

3. 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?..

4. 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.

5. 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

6. Sure thing! Let's do something like...

$\sqrt{ 24x^5y^7}$

7. before i reply to that, can you tell me how to make symbols so i can stop looking gimp with my typing lol

8. 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.

9. Originally Posted by Math Major
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 $x^2^(^2^) x^1$ ?

10. Sure, we can do this in steps. You are correct that

$x^5 = x^2 * x^2 * x$.

11. sorry i had to go on break at work

was i wrong for dividing the 24 down to 8?

12. You need to divide 24 by a perfect square. Try factoring it down and seeing if you can spot any.

13. 24/6 4..which is a perfect square

14. Correct. You've factored x and 24. You just need to factor y and then take the perfect square out of the radical.

15. Originally Posted by Greysoul
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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