
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 30th, 2017, 03:16 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 590 Thanks: 81  Equation With An Irrational Number
If 2x + x*(square root of 2) = 6, what is x?

November 30th, 2017, 03:21 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,534 Thanks: 513 Math Focus: Yet to find out. 
$x = \dfrac{6}{(2 + \sqrt{2})}$?

November 30th, 2017, 03:35 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
In a little more detail: $\displaystyle 2x+ x\sqrt{2}= (2+ \sqrt{2})x= 6$ Divide both sides by $\displaystyle 2+ \sqrt{2}$ If you don't like that $\displaystyle \sqrt{2}$ in the denominator, rationalize the denominator by multiplying by $\displaystyle \frac{2 \sqrt{2}}{2 \sqrt{2}}$: $\displaystyle \frac{6}{2+ \sqrt{2}}\frac{2 \sqrt{2}}{2 \sqrt{2}}= \frac{6(2 \sqrt{2})}{(2+ \sqrt{2})(2 \sqrt{2}}= \frac{12 6\sqrt{2}}{4 2}= 6 3\sqrt{2}$ 
November 30th, 2017, 03:55 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,829 Thanks: 762  
November 30th, 2017, 04:47 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,761 Thanks: 1009 Math Focus: Elementary mathematics and beyond  
November 30th, 2017, 04:54 PM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
I first misread the problem thinking that the "x" was inside the square root in which case squaring would be the way to go. But it is not, this is just a simple linear equation for x.


Tags 
equation, irrational, number 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
real number/irrational number  shaharhada  Number Theory  2  July 1st, 2017 09:31 AM 
irrational number multiplied by any real number  mick7  Number Theory  13  July 13th, 2015 10:08 PM 
Irrational Number  nfsmwbe  Number Theory  13  April 17th, 2012 07:17 AM 
What are the irrational number  MyNameIsVu  Number Theory  3  June 16th, 2009 08:13 PM 
Is pi irrational number?  habipermis  Algebra  5  December 28th, 2008 02:54 PM 