August 15th, 2014, 09:00 PM  #1 
Senior Member Joined: Jul 2014 From: Norway Posts: 140 Thanks: 3 Math Focus: geometry  Simplify
simplify  (3+sqrt(24))/(6 sqrt(8 ))

August 15th, 2014, 09:30 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Hello, girlbadatmath! Quote:
Note that: $\,\sqrt{24} \:=\:\sqrt{4\cdot 6} \:=\:\sqrt{4}\sqrt{6} \:=\:2\sqrt{6}$ And that: $\,6\sqrt{8} \:=\:6\sqrt{4\cdot2} \:=\:6\sqrt{4}\sqrt{2} \:=\:12\sqrt{2}$ The problem becomes: $\:\dfrac{3+2\sqrt{6}}{12\sqrt{2}}$ Multiply by $\frac{\sqrt{2}}{\sqrt{2}}:\;\dfrac{3 + 2\sqrt{6}}{12\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{ 2}} \;=\; \dfrac{3\sqrt{2} + 2\sqrt{12}}{12\cdot2} $ $\qquad =\;\dfrac{3\sqrt{2} + 2\sqrt{4\cdot3}}{24} \;=\;\dfrac{3\sqrt{2} + 2\sqrt{4}\sqrt{3}}{24} \;=\;\dfrac{3\sqrt{2} + 4\sqrt{3}}{24}$  
August 15th, 2014, 10:31 PM  #3 
Newbie Joined: Aug 2014 From: India Posts: 8 Thanks: 1 
Please click the below link.
Last edited by skipjack; August 17th, 2014 at 11:01 AM. Reason: Remove link 
August 16th, 2014, 12:09 AM  #4 
Senior Member Joined: Jul 2014 From: Norway Posts: 140 Thanks: 3 Math Focus: geometry 
Thank you so much!


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