Question

Simplify (2-sqrt(2+sqrt(3)))/(2+sqrt(2+sqrt(3)))

Answer 1

1+(4(sqrt(3)-8)(sqrt(2+sqrt(3))

Answer 2

How did you get that, @sara17 ?

Answer 3

Is this the problem, @omegawolf1000 ?
\[\Large \frac{ 2-\sqrt{2+\sqrt{3}} }{ 2+\sqrt{2+\sqrt{3}} } \]

Answer 4

This is a result of the half angle trip identity for tan if that helps. Need to simplify this to \[\sqrt(2+\sqrt3)*(2-\sqrt(2+\sqrt3))\]

Answer 5

Debbie that is the problem, learning this interface.

Answer 6

OK, that's fine - just wanted to make sure we were on the same page. And what you just showed above, you know that to be the correct answer?

Answer 7

Correct, I need to simplify it.

Answer 8

(2-sqrt(2+sqrt(3)))/(2+sqrt(2+sqrt(3))) ((2-sqrt(2+sqrt(3)))/(2-sqrt(2+sqrt(3)))
2-sqrt(3)-4sqrt(2+sqrt(3))/(2-sqrt(3))
((2-sqrt(3)-4sqrt(2+sqrt(3))/(2-sqrt(3))((2-sqrt(3))/2-sqrt(3))
=1+(4(sqrt(3)-8)(sqrt(2+sqrt(3))

Answer 9

Ok, thankfully found a solution. I took a wrong turn in my previous attempts by expanding the square of a number under a square root. I guess I am so use to expanding anything I see that I lost sight of my goal, aka get stuff out of the square root.

Answer 10

OK, well, glad you got it.... :) I wasn't getting too far, and I can't follow what @sara17 did.... I was trying something similar, but not getting that end result at all.

Answer 11

This is bugging me now... lol.... I only got this far, I guess I'm giving up now.

\[\Large \frac{ 2-\sqrt{2+\sqrt{3}} }{ 2+\sqrt{2+\sqrt{3}} }\cdot \frac{ 2-\sqrt{2+\sqrt{3}} }{ 2-\sqrt{2+\sqrt{3}} }=\frac{ 4-4\sqrt{2+\sqrt{3}}+(2+\sqrt{3}) }{ 4-(2+\sqrt{3}) }\]\[\Large =\frac{ 4-4\sqrt{2+\sqrt{3}}+(2+\sqrt{3}) }{ 2+\sqrt{3} }\]
\[\Large =\frac{ 4-4\sqrt{2+\sqrt{3}}}{ 2+\sqrt{3} }+\frac{2+\sqrt{3} }{ 2+\sqrt{3} }\]
\[\Large =\frac{ 4-4\sqrt{2+\sqrt{3}}}{ 2+\sqrt{3} }+1\]