AngelaB97
  • AngelaB97
how do you rationalize this denominator?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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AngelaB97
  • AngelaB97
|dw:1441582663963:dw|
caominhim
  • caominhim
apply the sqaure root to top and bottom
caominhim
  • caominhim
oh is the the 7th root?

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More answers

caominhim
  • caominhim
\[\sqrt[7]{\frac{ 1 }{ a^{2} }} = \frac{ \sqrt[7]{1} }{ \sqrt[7]{a^{2}} }\]
jdoe0001
  • jdoe0001
hmmm how would you rationalize ... say \(\bf \cfrac{1}{a^2}?\)
nincompoop
  • nincompoop
it is up to you \(\huge \frac{1^{\frac{1}{7}}}{(a^2)^\frac{1}{7}} \)
AngelaB97
  • AngelaB97
@nincompoop how would you work out the problem further?
jdoe0001
  • jdoe0001
by rationalizing, I assume you mean the exponent, as in \(\large a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\)
nincompoop
  • nincompoop
you can probably make it so there is no root in the denominator
AngelaB97
  • AngelaB97
the answer is supposed to be |dw:1441583091798:dw|
AngelaB97
  • AngelaB97
i just don't get how
nincompoop
  • nincompoop
mathematicians decided that it is inelegant to have a root in the denominator so we are suppose to stroke their egos
nincompoop
  • nincompoop
so multiply it by 1 that mimics the denominator
nincompoop
  • nincompoop
you know how \(\huge \frac{c}{c} =1\) or any fraction that has the same numerator and denominator equals 1 with the exception of \(\large \frac{0}{0} \)
nincompoop
  • nincompoop
were you told that's the answer by the book?
nincompoop
  • nincompoop
|dw:1441583625914:dw|
nincompoop
  • nincompoop
|dw:1441583819764:dw|
nincompoop
  • nincompoop
|dw:1441583873041:dw|
nincompoop
  • nincompoop
HELLOOOOOOOOO WHERE ARE YOUUUUUUUUUUUUUUUUU HELLOOOOOOOO ECHOOOOOOO
nincompoop
  • nincompoop
HELLOOOOOOOOO ECHOOOOOOOOO I think you fell into the mathematical abyss or black hole
AngelaB97
  • AngelaB97
okay i get what you did
AngelaB97
  • AngelaB97
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
nincompoop
  • nincompoop
i do not see it
AngelaB97
  • AngelaB97
|dw:1441588006576:dw|
AngelaB97
  • AngelaB97
why did they not put the rad sign over the 1 as well?
nincompoop
  • nincompoop
\(\huge 1^\frac{1}{7} = 1\)
nincompoop
  • nincompoop
the 7th root of 1 is 1 that is why
AngelaB97
  • AngelaB97
how I'm so sorry
nincompoop
  • nincompoop
what is the square root of 1 ?
AngelaB97
  • AngelaB97
1
nincompoop
  • nincompoop
what is the cube root of 1?
nincompoop
  • nincompoop
also 1
nincompoop
  • nincompoop
the trend follows
AngelaB97
  • AngelaB97
so anything to the nth root of 1 is 1
nincompoop
  • nincompoop
nth root providing it is a positive whole number, pretty much
nincompoop
  • nincompoop
I may need an actual mathematician to confirm this with proof, but that is what I know even tho I am not a mathematician
AngelaB97
  • AngelaB97
okay well thanks so much for your help! :)
nincompoop
  • nincompoop
no problem enjoy learning
AngelaB97
  • AngelaB97
thanks!

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