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AngelaB97

  • one year ago

how do you rationalize this denominator?

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  1. AngelaB97
    • one year ago
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    |dw:1441582663963:dw|

  2. caominhim
    • one year ago
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    apply the sqaure root to top and bottom

  3. caominhim
    • one year ago
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    oh is the the 7th root?

  4. caominhim
    • one year ago
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    \[\sqrt[7]{\frac{ 1 }{ a^{2} }} = \frac{ \sqrt[7]{1} }{ \sqrt[7]{a^{2}} }\]

  5. jdoe0001
    • one year ago
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    hmmm how would you rationalize ... say \(\bf \cfrac{1}{a^2}?\)

  6. nincompoop
    • one year ago
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    it is up to you \(\huge \frac{1^{\frac{1}{7}}}{(a^2)^\frac{1}{7}} \)

  7. AngelaB97
    • one year ago
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    @nincompoop how would you work out the problem further?

  8. jdoe0001
    • one year ago
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    by rationalizing, I assume you mean the exponent, as in \(\large a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\)

  9. nincompoop
    • one year ago
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    you can probably make it so there is no root in the denominator

  10. AngelaB97
    • one year ago
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    the answer is supposed to be |dw:1441583091798:dw|

  11. AngelaB97
    • one year ago
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    i just don't get how

  12. nincompoop
    • one year ago
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    mathematicians decided that it is inelegant to have a root in the denominator so we are suppose to stroke their egos

  13. nincompoop
    • one year ago
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    so multiply it by 1 that mimics the denominator

  14. nincompoop
    • one year ago
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    you know how \(\huge \frac{c}{c} =1\) or any fraction that has the same numerator and denominator equals 1 with the exception of \(\large \frac{0}{0} \)

  15. nincompoop
    • one year ago
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    were you told that's the answer by the book?

  16. nincompoop
    • one year ago
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    |dw:1441583625914:dw|

  17. nincompoop
    • one year ago
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    |dw:1441583819764:dw|

  18. nincompoop
    • one year ago
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    |dw:1441583873041:dw|

  19. nincompoop
    • one year ago
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    HELLOOOOOOOOO WHERE ARE YOUUUUUUUUUUUUUUUUU HELLOOOOOOOO ECHOOOOOOO

  20. nincompoop
    • one year ago
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    HELLOOOOOOOOO ECHOOOOOOOOO I think you fell into the mathematical abyss or black hole

  21. AngelaB97
    • one year ago
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    okay i get what you did

  22. AngelaB97
    • one year ago
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    however can you explain why the book only put the rad over the denominator and not the numerator...this is regarding the picute i attached up there

  23. nincompoop
    • one year ago
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    i do not see it

  24. AngelaB97
    • one year ago
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    |dw:1441588006576:dw|

  25. AngelaB97
    • one year ago
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    why did they not put the rad sign over the 1 as well?

  26. nincompoop
    • one year ago
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    \(\huge 1^\frac{1}{7} = 1\)

  27. nincompoop
    • one year ago
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    the 7th root of 1 is 1 that is why

  28. AngelaB97
    • one year ago
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    how I'm so sorry

  29. nincompoop
    • one year ago
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    what is the square root of 1 ?

  30. AngelaB97
    • one year ago
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    1

  31. nincompoop
    • one year ago
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    what is the cube root of 1?

  32. nincompoop
    • one year ago
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    also 1

  33. nincompoop
    • one year ago
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    the trend follows

  34. AngelaB97
    • one year ago
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    so anything to the nth root of 1 is 1

  35. nincompoop
    • one year ago
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    nth root providing it is a positive whole number, pretty much

  36. nincompoop
    • one year ago
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    I may need an actual mathematician to confirm this with proof, but that is what I know even tho I am not a mathematician

  37. AngelaB97
    • one year ago
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    okay well thanks so much for your help! :)

  38. nincompoop
    • one year ago
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    no problem enjoy learning

  39. AngelaB97
    • one year ago
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    thanks!

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