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November 13th, 2018, 11:32 AM  #1 
Newbie Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0  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 
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 timeywimey 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 Last edited by topsquark; November 13th, 2018 at 12:05 PM. 

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