Use pascals triangle to simplify:

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Use pascals triangle to simplify:

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Ok
\[(1+\sqrt2)^3\] Where do I start? Thanks in advance!
so you will start at the end the \[\sqrt{2}^{3}\]

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

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