anonymous
  • anonymous
4√(80x^17w^8)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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CoconutJJ
  • CoconutJJ
4 times sqrt of 4th root ?
anonymous
  • anonymous
?
CoconutJJ
  • CoconutJJ
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anonymous
  • anonymous
oh the second one
CoconutJJ
  • CoconutJJ
i c.... Assuming you're suppose to simplify, do you remember the exponent laws that apply to radicals
anonymous
  • anonymous
sorry not really
CoconutJJ
  • CoconutJJ
|dw:1439531324193:dw|
CoconutJJ
  • CoconutJJ
|dw:1439531372578:dw|
anonymous
  • anonymous
so divide x^17 by 4? like 17/4?
CoconutJJ
  • CoconutJJ
yes...
anonymous
  • anonymous
would i put it in a decimal form?
jtvatsim
  • jtvatsim
Here's an alternative way to think through these types of questions. First, think about the normal square roots. When you have square roots you need two factors inside in order to "escape" as in \[\sqrt{x^2} = \sqrt{x \cdot x} = x\] but if we only have one factor we are "trapped" \[\sqrt{2} = stuck\] Does that make sense so far?
anonymous
  • anonymous
yes
anonymous
  • anonymous
i got 2x^4w^4 4th√(5x^13 w^2) @jtvatsim
jtvatsim
  • jtvatsim
k let me check what you did. :)
jtvatsim
  • jtvatsim
You are close, just a few minor errors, but overall it seems like you have the idea. :)
anonymous
  • anonymous
can you tell me which part i got wrong?
jtvatsim
  • jtvatsim
Alright, so effectively we want to "bunch" our factors in groups of 4 whenever possible in order to escape the radical. We need groups of 4 because of the 4th root. \[\sqrt[4]{80x^{17}w^8} = \sqrt[4]{5\cdot2^4 \cdot x^4 \cdot x^4 \cdot x^4 \cdot x^4 \cdot x \cdot w^4 \cdot w^4} \] \[= 2\cdot x\cdot x \cdot x \cdot x \cdot w \cdot w\sqrt[4]{5x} = 2x^4w^2\sqrt[4]{5x}\]
anonymous
  • anonymous
ohhh that is much easier
jtvatsim
  • jtvatsim
Does that help you "see" it more clearly? I found that explanation to make the most sense when I was learning. :)
anonymous
  • anonymous
yes it helped a lot! thank you so much!
jtvatsim
  • jtvatsim
You are welcome! This same trick works no matter what root you are dealing with! Bring on the 100th roots, just bunch into groups of 100 (maybe not... don't give your teachers any ideas...) Have a good one! :)

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