Simplify the product A*B*C*D*E*F
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)))))
(In reply to
it is two easy by Ady TZIDON)
When combining E*F, under its radical, m=2 and n=sqrt(2+sqrt(2+sqrt(2+sqrt(2)))), so m^2n^2 = 4  2  sqrt(2+sqrt(2+sqrt(2))). Restoring the radical and simplifying gives sqrt(2sqrt(2+sqrt(2+sqrt(2)))).
Now when combining with D, we have a situation of (mn)(mn) or just the square, under the radical, cancelling that radical, so D*E*F = 2sqrt(2+sqrt(2+sqrt(2))).
But now we want to multiply this by C=sqrt(2sqrt(2+sqrt(2))), and it no longer falls into the category of either (m+n)(mn) or the square root of a square. I don't see where the answer can be obtained in 33 seconds.
A calculator shows the answer as
.0162298468649678...
but of course that's not very helpful in understanding the radical form.

Posted by Charlie
on 20050514 16:32:41 