Tia_Sweetheart17
  • Tia_Sweetheart17
square root of 512m^3. show work
Mathematics
katieb
  • katieb
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Rogue
  • Rogue
Radicals... In order to find the square root, we need to find a perfect square factor of 512. 64 is a perfect square factor, which can be multiplied by 8 to give 512. So we can write the square of 512 this way. \[\sqrt{512 m^3} = \sqrt{64 * 8 m^3}\]
Rogue
  • Rogue
\[\sqrt{64}*\sqrt{8 m^3} = 8 * \sqrt{4 * 2 m^3}\]
anonymous
  • anonymous
256 is also a perfect square factor :)

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Rogue
  • Rogue
\[8*\sqrt{4}*\sqrt{2 m^3} = 8*2*\sqrt{2 m^3} = 16\sqrt{2m^3}\]
Rogue
  • Rogue
Yeah, we could've skipped all that using 256, thanks Rick :)
Rogue
  • Rogue
The cube root of meters cubed is meters to the 1.5 power (yeah, I know, its weird). So you can write your final answer as:\[\sqrt{512 m^3} = 16\sqrt{2} m^{1.5}\]
Rogue
  • Rogue
Well, is that meters cubed, or is it a variable?
Rogue
  • Rogue
Either way, the answer is still the same.
anonymous
  • anonymous
I assume it's a variable
Rogue
  • Rogue
Yeah, makes more sense, meters to the 1.5 power, lol.
anonymous
  • anonymous
lol

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