General Math Question?

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Summary:

It's just a simple (or complicated to me) general math question. Related to radical simplification/rationalization.

General Math Question?

RogueEngineer 15 Jan 2014 03:24

Confused as to what’s going on here with simplification/rationalization of:
∜(256
∜(Fraction Bar) NOTE: ∜( Is over the whole fraction
∜(9x^6

whereas it goes to:
∜(9x^2
∜(Fraction Bar)
∜(x ∜(3^2 * x^2 * 3^2 * x^2 (Random x in front of bottom part?)

and Finally =
4∜(9x^2
∜(Fraction Bar)
3x^2

I understand that ∜256= 4 and then the bottom is multiplied by the bottom to cancel the 4th root which is ∜(3^2 * x^2 * 3^2 * x^2) then simplifies to ∜(81x^4 ) more simplified to 3x * x = 3x^2 (from the x in front). MY confusion IS WHERE does that other x in front come from? AND WHY does:

∜(16
∜(Fraction Bar)
∜(9x^2 equal the same thing? Again I get that ∜16=2 And 9x^2=3^2 * x^2 -(separated) then multiplied to cancel the 4th root.

Finally =
2∜(9x^2
∜(Fraction Bar)
3x

I just need to see the full expanded simplification of 9x^6 vs 9x^2. Is it 6-4 to get 3x^2? and where does that other x in front come from? I’m so confused…at least I understand all the other steps except for one.

Re: General Math Question?

Silver Phantom 15 Jan 2014 03:30

that x infront is really a simplification of saying that there was a x^4 in that root. this should clear up abit.

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The Silver Phantom welcomes you

Re: General Math Question?

RogueEngineer 15 Jan 2014 18:34

As in x^4 ∜(3^2 * x)? But the 4's cancel out then the x is multiplied over to make 3x^2. So that way it's taking out the highest numbers which is normal simplification rules. But then for 9x^2 I guess it's already simplified enough so the goal is cancel out the 4th root by multiplying. Therefore when it's 9x^6 it needs more simplification to get to the goal of canceling out the 4th root. So is that just subtracting? It gets weird with odd numbers too:
∜(81
∜(Fraction Bar)
∜(4x^7
becomes:
∜(3 * ∜(4x
∜(Fraction Bar)
∜(x ∜(2^2 * x^7 * 2^2 * x-(to get to 8?)
then simplifies to:
∜(16x^8 = 2x^2 that's divided by 4 not subtracted but I guess there's different rules for odd and even

Re: General Math Question?

RogueEngineer 16 Jan 2014 02:32

Haha yeah I forgot about the weird exponent fraction rule. It is dividing because its 6/4 = 1.5
So one goes in that's where the x comes from and then half is remaining that's where the x^2 on the inside comes from. I saw some youtube videos on it.