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anonymous

  • 5 years ago

3nth sqrt (x-9)^3

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  1. anonymous
    • 5 years ago
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    \[(\sqrt[3]{x-9})^3\] If you cube a cubed root you just remove them both. \[\sqrt[3]{a^3} = \sqrt[3]{a}^3 = a^{\frac{3}{3}} = a^1 = a \]

  2. anonymous
    • 5 years ago
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    its whats inside the radical thats confusing me

  3. anonymous
    • 5 years ago
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    x - 9 is just x - 9

  4. anonymous
    • 5 years ago
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    Or do I misunderstand your question?

  5. anonymous
    • 5 years ago
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    well. i have another problem thats like that and i just dont know what to do with (x-anything)^anything

  6. anonymous
    • 5 years ago
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    Just expand it and simplify as much as possible. Unless you have an equal there you can't really solve for x.

  7. anonymous
    • 5 years ago
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    so you foil within the radical to expand it?

  8. anonymous
    • 5 years ago
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    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.

  9. anonymous
    • 5 years ago
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    so the answer is just x-9

  10. anonymous
    • 5 years ago
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    Yep.

  11. anonymous
    • 5 years ago
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    Assuming that it is as I have it written originally.

  12. anonymous
    • 5 years ago
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    thank you, can you help me with sqrt 25(x+2)^4

  13. anonymous
    • 5 years ago
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    Of course.

  14. anonymous
    • 5 years ago
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    Can you quickly rewrite each of those factors as a square?

  15. anonymous
    • 5 years ago
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    25 is what squared?

  16. anonymous
    • 5 years ago
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    5

  17. anonymous
    • 5 years ago
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    And \((x+2)^4 \) is what squared?

  18. anonymous
    • 5 years ago
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    that i dont know

  19. anonymous
    • 5 years ago
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    Oh. well what if I asked you what \((2^2)^2\) was. Do you know that?

  20. anonymous
    • 5 years ago
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    wouldnt that be 16?

  21. anonymous
    • 5 years ago
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    Yes, but don't think about it that way ;p

  22. anonymous
    • 5 years ago
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    Think about it as \(2^4\)

  23. anonymous
    • 5 years ago
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    When you raise a power to a power you multiply the exponents

  24. anonymous
    • 5 years ago
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    Have you been taught this?

  25. anonymous
    • 5 years ago
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    the teacher i have sucks. so probably have but not the way your explaining it

  26. anonymous
    • 5 years ago
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    Hrm. Ok, well so if raising something to a power multiplies exponents, then taking the root of a power divides the exponent.

  27. anonymous
    • 5 years ago
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    For example. \[\sqrt{5^4} = 5^2\] \[\sqrt[3]{7^{12}} = 7^4\] etc.

  28. anonymous
    • 5 years ago
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    So if you have \[\sqrt{a^4} =\ ?\]

  29. anonymous
    • 5 years ago
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    okaie. so would (x+2)^4 would just be x+2 ^ 2. and the answer to your question is a^2

  30. anonymous
    • 5 years ago
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    Yes precisely. So for your problem you had \[\sqrt{5^2(x+2)^4} =\ ?\]

  31. anonymous
    • 5 years ago
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    well it was 25 which = 5^2.

  32. anonymous
    • 5 years ago
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    Right. Same difference, so take the square root of that and you get?

  33. anonymous
    • 5 years ago
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    5(x+2)^2

  34. anonymous
    • 5 years ago
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    Exactly.

  35. anonymous
    • 5 years ago
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    THANKK YOU SO MUCH<!!!!

  36. anonymous
    • 5 years ago
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    Very welcome ! =)

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