Question

Please help me simplify this

Answer 1

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

Answer 2

`\sqrt{2 \: + \: √(3) } \: + \: \sqrt{2 \: - \: √(3) } \: - \: \sqrt{3 \: + \: 2 √(2) } \: - \: \sqrt{3 \: - \: 2 √(2) }`

`\sqrt{2 + √(3) } \: + \: \sqrt{2 - √(3) } \: - \: \sqrt{ { (√(2 ) + 1) }^(2) } \: - \: \sqrt{ {( √(2) - 1) }^(2) }`

`\sqrt{2 \: + \: √(3) } \: + \: \sqrt{2 \: - \: √(3) } \: - \: 2 √(2) \: = \: - 0.378937`