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anonymous

  • one year ago

Simplify

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  1. anonymous
    • one year ago
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    \[\frac{ \sqrt[4]{400} }{ \sqrt[4]{5}}\]

  2. anonymous
    • one year ago
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    Please explain/show your work so i understand

  3. anonymous
    • one year ago
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    @dan815

  4. anonymous
    • one year ago
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    @Michele_Laino

  5. Michele_Laino
    • one year ago
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    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

  6. anonymous
    • one year ago
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    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

  7. Michele_Laino
    • one year ago
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    what is: 25/5=...?

  8. anonymous
    • one year ago
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    5

  9. Michele_Laino
    • one year ago
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    ok! so we can write this: \[\frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = \sqrt[4]{{5 \times 16}}\]

  10. Michele_Laino
    • one year ago
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    \[\large \frac{{\sqrt[4]{{400}}}}{{\sqrt[4]{5}}} = \sqrt[4]{{\frac{{400}}{5}}} = \sqrt[4]{{\frac{{25 \times 16}}{5}}} = \sqrt[4]{{5 \times 16}}\]

  11. Michele_Laino
    • one year ago
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    next, please keep in mind that: \[\Large 16 = {2^4}\]

  12. anonymous
    • one year ago
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    ok so what do we do with the 16 than?

  13. Michele_Laino
    • one year ago
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    here is the next step: \[\Large \sqrt[4]{{5 \times 16}} = \sqrt[4]{5} \times \sqrt[4]{{16}} = \sqrt[4]{5} \times \sqrt[4]{{{2^4}}}\]

  14. anonymous
    • one year ago
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    Where did the 25 come from? like when you splits it to 25x16 how did you get those numbers?

  15. Michele_Laino
    • one year ago
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    since: \[\Large 400 = 25 \times 16\]

  16. anonymous
    • one year ago
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    Ok i see now

  17. Michele_Laino
    • one year ago
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    step by step: \[\large 400 = 4 \times 100 = 4 \times \left( {4 \times 25} \right) = \left( {4 \times 4} \right) \times 25 = 16 \times 25\]

  18. Michele_Laino
    • one year ago
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    now, do you know how to simplify: \[\Large \sqrt[4]{{{2^4}}}\]?

  19. anonymous
    • one year ago
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    Sorry im catching up my computer froze

  20. anonymous
    • one year ago
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    \[2\sqrt[4]{5}\]

  21. Michele_Laino
    • one year ago
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    that's right, since: \[\Large \sqrt[4]{{{2^4}}} = {2^{4/4}} = {2^1} = 2\]

  22. Michele_Laino
    • one year ago
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    or you can use windows calculator, to compute this: \[\Large \sqrt[4]{{{2^4}}} = \sqrt[4]{{16}} = 2\]

  23. anonymous
    • one year ago
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    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

  24. Michele_Laino
    • one year ago
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    :)

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