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Jadedry

  • one year ago

Use pascals triangle to simplify:

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  1. anonymous
    • one year ago
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    Ok

  2. Jadedry
    • one year ago
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    \[(1+\sqrt2)^3\] Where do I start? Thanks in advance!

  3. anonymous
    • one year ago
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    so you will start at the end the \[\sqrt{2}^{3}\]

  4. Jadedry
    • one year ago
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    Okay.

  5. Jadedry
    • one year ago
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    I should end up with: \[1 + (3 + 3\sqrt2) + (3+6) + 2^{1.5}\] right? But my textbook says: \[7+ 5\sqrt2\] how?

  6. FireKat97
    • one year ago
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    i dont understand why you're adding... but the idea seems to be there, here is my working out \[1(1)^3 + 3(1)^2(\sqrt{2}) + 3(1)(\sqrt{2} )^2 + (\sqrt{2} )^3\]

  7. FireKat97
    • one year ago
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    and that simplifies down to \[7 + 5\sqrt{2}\]

  8. FireKat97
    • one year ago
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    @Jadedry do you see why I did what I did?

  9. anonymous
    • one year ago
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    so you will start at the end the 2√3

  10. Jadedry
    • one year ago
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    @FireKat97 Hello again, Firekat! You're absolutely right, I added when I should have multiplied. X.X Once question though, how does\[\sqrt 2 ^{3} = 2 \sqrt 2 ?\]

  11. FireKat97
    • one year ago
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    okay so you know how you have \[(\sqrt{2})^3\] that opens up to \[\sqrt{2}. \sqrt{2}. \sqrt{2}\] and when you multiply a root by itself, the roots cancel, so you get left with \[2\sqrt{2}\]

  12. FireKat97
    • one year ago
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    I hope that makes sense

  13. FireKat97
    • one year ago
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    and hey @Jadedry lol

  14. Jadedry
    • one year ago
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    Ah that makes perfect sense I understand. ;u; Thanks for the help! closing this now!

  15. FireKat97
    • one year ago
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    no problem :)

  16. FireKat97
    • one year ago
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    But even when you had \[2^{3/2}\] you can break that down to \[2^1.2^{1/2}\] which is again \[2 \sqrt{2}\] so thats another way to think about it @Jadedry :)

  17. Jadedry
    • one year ago
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    @FireKat97 Ooo! I got that. Interesting way of looking at it. thanks again. ;u;

  18. FireKat97
    • one year ago
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    @Jadedry no problem :)

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