anonymous
  • anonymous
what is this?? sqrt27u^3v^10w^6
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Owlcoffee
  • Owlcoffee
\[\sqrt{27u^3 v^10 w^6}\] Like this?
anonymous
  • anonymous
almost. its v to the tenth

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Owlcoffee
  • Owlcoffee
okay, what do you want to with that?
anonymous
  • anonymous
it says simplify the expression
anonymous
  • anonymous
and assume all variables are positive
Owlcoffee
  • Owlcoffee
\[\sqrt{27u^3v ^{10}w^6}\] Here you can take advantage of a property of radicals: \[\sqrt{u.v}=\sqrt{u}\sqrt{v}\] Si, here, we can take the square root of each factor: \[\sqrt{27u^3v ^{10}w^6}=\sqrt{27}\sqrt{u^3}\sqrt{v ^{10}}\sqrt{w^6}\]
anonymous
  • anonymous
oh okay. yeah I remember learning that. but is that the answer?? arent there supposed to to be like, exponents and fractions and stuff?
anonymous
  • anonymous
dont you do like (27u^3v^10x^6)^1/2
Owlcoffee
  • Owlcoffee
Yes, but I will not give you the answer, I am not allowed to do that.
anonymous
  • anonymous
i dont know where to go from there
anonymous
  • anonymous
i know you cant give the answer. but would you be willing to help me? I dont know where to go after (27u^v^10w^6)^1/2
Owlcoffee
  • Owlcoffee
If you want to take the method if expressing the main radical as a fractionary exponent, you can take advantage of a exponential property: \[(27u^3v ^{10}w^6)^{\frac{ 1 }{ 2 }}\] \[(a^n)^m=a ^{mn}\] This expands to each factor, so: \[(27^{\frac{ 1 }{ 2 }})(u ^{3\frac{ 1 }{ 2 }})(v ^{10\frac{ 1 }{ 2 }})(w ^{6\frac{ 1 }{ 2 }})\]
anonymous
  • anonymous
and then what? @owlcoffee
Owlcoffee
  • Owlcoffee
simplify the exponents.

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