
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 13th, 2018, 10:32 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, 11:03 AM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 928 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 11:05 AM. 

Tags 
degree, expression, higher, root 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Solving Congruence Equation of Higher Degree  pritampallab  Algebra  1  August 20th, 2018 08:41 PM 
continued fraction expression for root 2 in Q_7  maximus101  Number Theory  0  November 8th, 2012 02:43 PM 
Higher degree function  ilovetheflowguy  Algebra  1  April 23rd, 2012 02:31 AM 
What is the degree of a square root?  EkajArmstro  Algebra  3  March 29th, 2011 09:19 AM 
Computing higher degree derivatives: hard problem  julien  Real Analysis  0  May 3rd, 2007 01:56 AM 