Jadedry
  • Jadedry
Use pascals triangle to simplify:
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Ok
Jadedry
  • Jadedry
\[(1+\sqrt2)^3\] Where do I start? Thanks in advance!
anonymous
  • anonymous
so you will start at the end the \[\sqrt{2}^{3}\]

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Jadedry
  • Jadedry
Okay.
Jadedry
  • Jadedry
I should end up with: \[1 + (3 + 3\sqrt2) + (3+6) + 2^{1.5}\] right? But my textbook says: \[7+ 5\sqrt2\] how?
FireKat97
  • FireKat97
i dont understand why you're adding... but the idea seems to be there, here is my working out \[1(1)^3 + 3(1)^2(\sqrt{2}) + 3(1)(\sqrt{2} )^2 + (\sqrt{2} )^3\]
FireKat97
  • FireKat97
and that simplifies down to \[7 + 5\sqrt{2}\]
FireKat97
  • FireKat97
@Jadedry do you see why I did what I did?
anonymous
  • anonymous
so you will start at the end the 2√3
Jadedry
  • Jadedry
@FireKat97 Hello again, Firekat! You're absolutely right, I added when I should have multiplied. X.X Once question though, how does\[\sqrt 2 ^{3} = 2 \sqrt 2 ?\]
FireKat97
  • FireKat97
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 \[2\sqrt{2}\]
FireKat97
  • FireKat97
I hope that makes sense
FireKat97
  • FireKat97
and hey @Jadedry lol
Jadedry
  • Jadedry
Ah that makes perfect sense I understand. ;u; Thanks for the help! closing this now!
FireKat97
  • FireKat97
no problem :)
FireKat97
  • FireKat97
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 :)
Jadedry
  • Jadedry
@FireKat97 Ooo! I got that. Interesting way of looking at it. thanks again. ;u;
FireKat97
  • FireKat97
@Jadedry no problem :)

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