anonymous
  • anonymous
Simplify
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ \sqrt[4]{400} }{ \sqrt[4]{5}}\]
anonymous
  • anonymous
Please explain/show your work so i understand
anonymous
  • anonymous
@dan815

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anonymous
  • anonymous
@Michele_Laino
Michele_Laino
  • Michele_Laino
hint: we can write: \[\Large \frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = ...\] please continue
anonymous
  • anonymous
I dont know how to square this, I'm totally lost lol that's why i need the help and for someone to explain how we get to the answer
Michele_Laino
  • Michele_Laino
what is: 25/5=...?
anonymous
  • anonymous
5
Michele_Laino
  • Michele_Laino
ok! so we can write this: \[\frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = \sqrt[4]{{5 \times 16}}\]
Michele_Laino
  • Michele_Laino
\[\large \frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = \sqrt[4]{{5 \times 16}}\]
Michele_Laino
  • Michele_Laino
next, please keep in mind that: \[\Large 16 = {2^4}\]
anonymous
  • anonymous
ok so what do we do with the 16 than?
Michele_Laino
  • Michele_Laino
here is the next step: \[\Large \sqrt[4]{{5 \times 16}} = \sqrt[4]{5} \times \sqrt[4]{{16}} = \sqrt[4]{5} \times \sqrt[4]{{{2^4}}}\]
anonymous
  • anonymous
Where did the 25 come from? like when you splits it to 25x16 how did you get those numbers?
Michele_Laino
  • Michele_Laino
since: \[\Large 400 = 25 \times 16\]
anonymous
  • anonymous
Ok i see now
Michele_Laino
  • Michele_Laino
step by step: \[\large 400 = 4 \times 100 = 4 \times \left( {4 \times 25} \right) = \left( {4 \times 4} \right) \times 25 = 16 \times 25\]
Michele_Laino
  • Michele_Laino
now, do you know how to simplify: \[\Large \sqrt[4]{{{2^4}}}\]?
anonymous
  • anonymous
Sorry im catching up my computer froze
anonymous
  • anonymous
\[2\sqrt[4]{5}\]
Michele_Laino
  • Michele_Laino
that's right, since: \[\Large \sqrt[4]{{{2^4}}} = {2^{4/4}} = {2^1} = 2\]
Michele_Laino
  • Michele_Laino
or you can use windows calculator, to compute this: \[\Large \sqrt[4]{{{2^4}}} = \sqrt[4]{{16}} = 2\]
anonymous
  • anonymous
Sweet, thank you very ,much for guiding me along instead of giving me the answer, i like to understand how to get to the answer
Michele_Laino
  • Michele_Laino
:)

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