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August 15th, 2014, 10:00 PM   #1
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Simplify

simplify | (3+sqrt(24))/(6 sqrt(8 ))
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August 15th, 2014, 10:30 PM   #2
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Hello, girlbadatmath!

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} $

$\qquad =\;\dfrac{3\sqrt{2} + 2\sqrt{4\cdot3}}{24} \;=\;\dfrac{3\sqrt{2} + 2\sqrt{4}\sqrt{3}}{24} \;=\;\dfrac{3\sqrt{2} + 4\sqrt{3}}{24}$
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August 15th, 2014, 11:31 PM   #3
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Please click the below link.

Last edited by skipjack; August 17th, 2014 at 12:01 PM. Reason: Remove link
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August 16th, 2014, 01:09 AM   #4
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Thank you so much!
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