anonymous
  • anonymous
Find The Value Of: The Square Root Of 24 Over 4 Times The Square Root Of 5.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[\frac{\sqrt{24}}{4}\times \sqrt{5}\]
anonymous
  • anonymous
\[\sqrt{24}/4\sqrt{5}=\sqrt{6*4}/4\sqrt{5}=2\sqrt{6}/4\sqrt{5}=\sqrt{6}/\sqrt{5}=\sqrt{30}/5\]
anonymous
  • anonymous
or \[\frac{\sqrt{24}}{4\sqrt{5}}\]?

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anonymous
  • anonymous
ups, 2 missing in the denominator \[\sqrt{30}/10\]
Kainui
  • Kainui
\[\sqrt{24}/(4\sqrt{5})\] So first off, what can we take out of the square root? It looks like \[\sqrt{24}=\sqrt{2*2*2*3}=2\sqrt{6}\] Since 2*2 is just 4, we can take the square root and bring a 2 out front, but the 2 and 3 stay behind since they're not squares. Using some exponent rules, since everything is multiplied together.\[2\sqrt{6}/4\sqrt{5}=(1/2)\sqrt{6/5}\]

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