anonymous
  • anonymous
Medal to most helpful. Simplify 2 times the 4th root of 80. Thanks.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[2 \sqrt[4]{80}\]
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{80} }\)
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{80} }\) \(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16\times5} }\) \(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16}\times\sqrt[4]{5} }\)

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More answers

SolomonZelman
  • SolomonZelman
Can you go from there?
anonymous
  • anonymous
Could you continue from there, please? @SolomonZelman
SolomonZelman
  • SolomonZelman
Do you know what "forth root" means?
anonymous
  • anonymous
one fourth power
anonymous
  • anonymous
2 * 16^1/4 * 5^1/4 ??
SolomonZelman
  • SolomonZelman
But that second component is integer when simplified.
SolomonZelman
  • SolomonZelman
I will try to make the definition clear through one example. Just stay with me please
SolomonZelman
  • SolomonZelman
You know that, \(\large\color{#000000 }{ \displaystyle 3\times 3\times 3\times 3 =81 }\) Ok?
anonymous
  • anonymous
okay
SolomonZelman
  • SolomonZelman
Ok, good, and how many times did I multiply the 3?
anonymous
  • anonymous
4 times
SolomonZelman
  • SolomonZelman
Yes
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle \underbrace{3\times 3\times 3\times 3 }_{4~\rm times}=81 }\)
anonymous
  • anonymous
I'm following.
SolomonZelman
  • SolomonZelman
And that would mean \(\large\color{#000000 }{ \displaystyle 3^4=81 }\)
SolomonZelman
  • SolomonZelman
And the inverse operation of \(\large\color{#000000 }{ \displaystyle 3^4=81 }\), is, \(\Large\color{#000000 }{ \displaystyle \sqrt[\color{red}{4}]{81} =3}\)
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle \sqrt[4]{81}=3 }\) and/because \(\large\color{#000000 }{ \displaystyle 3^4=81 }\) So, this way, \(\large\color{#000000 }{ \displaystyle \sqrt[4]{16}={\bf \quad is~?} }\)
SolomonZelman
  • SolomonZelman
(try dividing 16 by 2 a bunch of times and tell me that 2^what? = 16)
anonymous
  • anonymous
Answer Choices: (Just for reference) A. \[4\sqrt[4]{5}\] B. \[8\sqrt[4]{5}\] C. \[16\sqrt[4]{5}\] D. \[32\sqrt[4]{5}\]
SolomonZelman
  • SolomonZelman
(This way you would be able to determine the 4th root of 16)
anonymous
  • anonymous
2?
SolomonZelman
  • SolomonZelman
Explain your question
anonymous
  • anonymous
sorry it took so long i had to refresh openstudy
anonymous
  • anonymous
the answer to your question is 2. the fourth root of 16
SolomonZelman
  • SolomonZelman
Yes, the 4th root of 16 is 2.
SolomonZelman
  • SolomonZelman
So let's come back to our problem.
anonymous
  • anonymous
okay
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{80} }\) \(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16\times5} }\) \(\large\color{#000000 }{ \displaystyle 2\cdot \sqrt[4]{16}\times\sqrt[4]{5} }\) this is where we left.
anonymous
  • anonymous
yep
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle 2\cdot \color{red}{2}\times\sqrt[4]{5} }\)
SolomonZelman
  • SolomonZelman
So your most simplified answer is?
SolomonZelman
  • SolomonZelman
(Note that there is NO way to simplify \(\large\color{#000000 }{ \sqrt[4]{5} }\))
anonymous
  • anonymous
\[4\sqrt[4]{5}\]
SolomonZelman
  • SolomonZelman
Yup, that's exactly right!
anonymous
  • anonymous
Okay, thank you for your help! I appreciate it. Cheers!
SolomonZelman
  • SolomonZelman
YW

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