## Jadedry one year ago Use pascals triangle to simplify:

1. anonymous

Ok

$(1+\sqrt2)^3$ Where do I start? Thanks in advance!

3. anonymous

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

Okay.

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

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

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

8. FireKat97

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

9. anonymous

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$\sqrt 2 ^{3} = 2 \sqrt 2 ?$

11. 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 $2\sqrt{2}$

12. FireKat97

I hope that makes sense

13. FireKat97

Ah that makes perfect sense I understand. ;u; Thanks for the help! closing this now!

15. FireKat97

no problem :)

16. 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 :)

@FireKat97 Ooo! I got that. Interesting way of looking at it. thanks again. ;u;

18. FireKat97