Question

I need to prove this is a natural number, but don't say the answer please, I just want the first step.

Answer 1

\[\sqrt{7 + 4\sqrt{3}} + \sqrt{7 - 4\sqrt{3}}\]

Answer 2

Start by multiplying the expression by \[\sqrt{7-\sqrt{3}} \div \sqrt{7-\sqrt{3}}\]

Answer 3

*sorry, the root 3's should be 4*root 3

Answer 4

Okay, and all negative?

Answer 5

yes, you're multiplying the expression by 1, but then stuff starts canceling out :)

Answer 6

Can I call 7 a and 4qsrt3 b?

Answer 7

If that makes it easier for you, I guess. So long as you realize a^2-b^2=1 :)

Answer 8

Okay, let me try

Answer 9

Omg, I got it! It's 14. Idk if it's right but it looks right

Answer 10

Aww according to wolfram it is 4. At least I got close

Answer 11

Can you help me, @SmoothMath ?

Answer 12

I can show you my work if you want