anonymous
  • anonymous
3nth sqrt (x-9)^3
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[(\sqrt[3]{x-9})^3\] If you cube a cubed root you just remove them both. \[\sqrt[3]{a^3} = \sqrt[3]{a}^3 = a^{\frac{3}{3}} = a^1 = a \]
anonymous
  • anonymous
its whats inside the radical thats confusing me
anonymous
  • anonymous
x - 9 is just x - 9

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anonymous
  • anonymous
Or do I misunderstand your question?
anonymous
  • anonymous
well. i have another problem thats like that and i just dont know what to do with (x-anything)^anything
anonymous
  • anonymous
Just expand it and simplify as much as possible. Unless you have an equal there you can't really solve for x.
anonymous
  • anonymous
so you foil within the radical to expand it?
anonymous
  • anonymous
Well if it's something cubed inside a cubed root, there's no need to foil it cause the two cancel eachother out. Otherwise yeah you'd have to distribute (foil) and hope it turns out nicely.
anonymous
  • anonymous
so the answer is just x-9
anonymous
  • anonymous
Yep.
anonymous
  • anonymous
Assuming that it is as I have it written originally.
anonymous
  • anonymous
thank you, can you help me with sqrt 25(x+2)^4
anonymous
  • anonymous
Of course.
anonymous
  • anonymous
Can you quickly rewrite each of those factors as a square?
anonymous
  • anonymous
25 is what squared?
anonymous
  • anonymous
5
anonymous
  • anonymous
And \((x+2)^4 \) is what squared?
anonymous
  • anonymous
that i dont know
anonymous
  • anonymous
Oh. well what if I asked you what \((2^2)^2\) was. Do you know that?
anonymous
  • anonymous
wouldnt that be 16?
anonymous
  • anonymous
Yes, but don't think about it that way ;p
anonymous
  • anonymous
Think about it as \(2^4\)
anonymous
  • anonymous
When you raise a power to a power you multiply the exponents
anonymous
  • anonymous
Have you been taught this?
anonymous
  • anonymous
the teacher i have sucks. so probably have but not the way your explaining it
anonymous
  • anonymous
Hrm. Ok, well so if raising something to a power multiplies exponents, then taking the root of a power divides the exponent.
anonymous
  • anonymous
For example. \[\sqrt{5^4} = 5^2\] \[\sqrt[3]{7^{12}} = 7^4\] etc.
anonymous
  • anonymous
So if you have \[\sqrt{a^4} =\ ?\]
anonymous
  • anonymous
okaie. so would (x+2)^4 would just be x+2 ^ 2. and the answer to your question is a^2
anonymous
  • anonymous
Yes precisely. So for your problem you had \[\sqrt{5^2(x+2)^4} =\ ?\]
anonymous
  • anonymous
well it was 25 which = 5^2.
anonymous
  • anonymous
Right. Same difference, so take the square root of that and you get?
anonymous
  • anonymous
5(x+2)^2
anonymous
  • anonymous
Exactly.
anonymous
  • anonymous
THANKK YOU SO MUCH
anonymous
  • anonymous
Very welcome ! =)

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