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November 13th, 2018, 11:32 AM   #1
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higher degree root expression

what is the result of the expression in the attached?

and how can i write these root signs here? i could not

i tried to take in 1/3 root parantheses or other roots but didnt work
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November 13th, 2018, 12:03 PM   #2
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Math Focus: Wibbly wobbly timey-wimey stuff.
We need to rationalize the denominator of the first term.

Note that $\displaystyle 9^{1/3} = (3^2)^{1/3}$. Then the denominator of the first term is $\displaystyle (3^2)^{1/3} + (3)^{1/3} + 1$.

Here's an identity you may not have seen before. (Multiply it out to see why.)
$\displaystyle (a - 1)(a^2 + a + 1) = a^3 - 1$

So let $\displaystyle a = 3^{1/3}$ and we get
$\displaystyle ((3)^{1/3} - 1)((3^{1/3})^2 + (3^{1/3}) + 1) = (3^{1/3})^3 - 1 = 3 - 1$

In order to rationalize the first term, then, we multiply the numerator and denominator by $\displaystyle 3^{1/3} - 1$.

Can you finish?

-Dan
Thanks from MarkFL and JeffM1

Last edited by topsquark; November 13th, 2018 at 12:05 PM.
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