Question

Please help me simplify this

Answer 1

$\sqrt{2 \: + \: \sqrt{3} } \: + \: \sqrt{2 \: - \: \sqrt{3} } \: - \: \sqrt{3 \: + \: 2 \sqrt{2} } \: - \: \sqrt{3 \: - \: 2 \sqrt{2} }$
$\sqrt{2 + \sqrt{3} } \: + \: \sqrt{2 - \sqrt{3} } \: - \: \sqrt{ { (\sqrt{2 } + 1) }^{2} } \: - \: \sqrt{ {( \sqrt{2} - 1) }^{2} }$
$\sqrt{2 \: + \: \sqrt{3} } \: + \: \sqrt{2 \: - \: \sqrt{3} } \: - \: 2 \sqrt{2} \: = \: - 0.378937$

Answer 2

Answer:

Step-by-step explanation:

the idea is

by assuming that (2+sqrt(3)) = a^2 + 2ab + b^2

let 2ab = sqrt(3) , then b =sqrt(3)/2a   (i)

let a^2 +b^2 = 2     (ii)

then substitute by (i) in (ii) and get a and b

then do this for every sqrt in your ask

finally you will get your answer