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 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
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Joined: Dec 2006
From: Lexington, MA

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Quote:
 Simplify: $\:\dfrac{3+\sqrt{24}}{6\sqrt{8}}$

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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