A = (√2)
B = (√(2-√2))
C = (√(2-√(2+√2)))
D = (√(2-√(2+√(2+√2))))
E = (√(2-√(2+√(2+√(2+√2)))))
F = (√(2+√(2+√(2+√(2+√2)))))

Let M = sqrt(2 + sqrt(2)).

M^2 = 2 + sqrt(2)

E * F = sqrt(4 - (2 + sqrt(2 + sqrt(2 + sqrt(2))))) =

= sqrt(2 - sqrt(2 + sqrt(2 + sqrt(2)))) = D.

D * E * F = D^2 = 2 - sqrt(2 + sqrt(2 + sqrt(2)))

D * E * F = 2 - sqrt(2 + M)

C = sqrt(2 - M)

C * D * E * F = sqrt(2 + M) * sqrt(2 - M) = sqrt (4 - M^2) =

= sqrt(4 - 2 - sqrt(2)) = sqrt(2 - sqrt(2)) = B

B * C * D * E * F = B^2 = 2 - sqrt(2)

A * B * C * D * E * F = sqrt(2) * [2 - sqrt(2)] = 2* sqrt(2) - 2 =

=2,8284 - 2 = 0,8284...