anonymous
  • anonymous
Square root of (4x^6)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
sqrt(4) * x^(6/2)
JamesJ
  • JamesJ
No, not zero.
JamesJ
  • JamesJ
Simplify what amistre has written

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anonymous
  • anonymous
Why did he divide the 6 by 2..?
amistre64
  • amistre64
those root radicals are just exponents
amistre64
  • amistre64
2rt() = ^1/2 10rt() = ^1/10
JamesJ
  • JamesJ
because \[ (x^a)^b = x^{ab} \] Hence \[ \sqrt{x^6} = (x^6)^{1/2} = x^{6/2} = ... \]
amistre64
  • amistre64
its makes the math simpler
JamesJ
  • JamesJ
Hence here \[ \sqrt{4x^6} = \sqrt{4} \sqrt{x^6} = ... what? \]
anonymous
  • anonymous
I still don't get where the 1/2 is coming from
JamesJ
  • JamesJ
\[ \sqrt{x} = x^{1/2} \] For example, if \[ \sqrt{x} = 3 \] then \[ \sqrt{x}^2 = 3^2 \] i.e., \[ x = 3^2 \] It must be therefore that \( \sqrt{x} = x^{1/2} \). If this weren't the case we wouldn't have \[ \sqrt{x}^2 = x \] Having \[ \sqrt{x} = x^{1/2} \] is consistent with the definition of square root because \[ (x^{1/2})^2 = x^{2/2} = x^1 = x \]
anonymous
  • anonymous
So am i only dividing the x^6 by two to make it x^3 since the exponent doesn't pertain to the 4?

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