My Math Forum higher degree root expression

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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 Math Team     Joined: May 2013 From: The Astral plane Posts: 1,915 Thanks: 774 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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