Question

Use pascals triangle to simplify:

Answer 1

Ok

Answer 2

\[(1+\sqrt2)^3\]

Where do I start?

Thanks in advance!

Answer 3

so you will start at the end the \[\sqrt{2}^{3}\]

Answer 4

Okay.

Answer 5

I should end up with:

\[1 + (3 + 3\sqrt2) + (3+6) + 2^{1.5}\] right?

But my textbook says:

\[7+ 5\sqrt2\]

how?

Answer 6

i dont understand why you're adding... but the idea seems to be there, here is my working out

\[1(1)^3 + 3(1)^2(\sqrt{2}) + 3(1)(\sqrt{2} )^2 + (\sqrt{2} )^3\]

Answer 7

and that simplifies down to \[7 + 5\sqrt{2}\]

Answer 8

@Jadedry do you see why I did what I did?

Answer 9

so you will start at the end the
2√3

Answer 10

@FireKat97

Hello again, Firekat!

You're absolutely right, I added when I should have multiplied. X.X

Once question though, how does\[\sqrt 2 ^{3} = 2 \sqrt 2 ?\]

Answer 11

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 \[2\sqrt{2}\]

Answer 12

I hope that makes sense

Answer 13

and hey @Jadedry lol

Answer 14

Ah that makes perfect sense I understand. ;u;

Thanks for the help! closing this now!

Answer 15

no problem :)

Answer 16

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 :)

Answer 17

@FireKat97

Ooo! I got that. Interesting way of looking at it. thanks again. ;u;

Answer 18

@Jadedry no problem :)