Thereby reenacting one of my favorite denestings:
1/5 3/5 3/5 2/5 1/5 2/5 3/5 1/5 1/3 - 2 3 + 2 3 + 3 + 2 (3 - 2 ) = ------------------------------------- , 2/3 5
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The ^1/3 has already been highlighted. So far, I've only seen the numeric verifications, but surely a symbolic one would be more appropriate?
verification doesn't require computer algebra. it took me less than half a page to calculate and simplify (3^(1/5) + 4^(1/5) - 54^(1/5) + 72^(1/5))^3 with pen and paper. contrast this to FINDING the identity!
mike
Amen. I've now tried ~ 10^8 cases of (a^(1/5)-b^(1/5))^(1/3) without further success, and for sqrt, only 3/5 4/5 3/5 2/5 2/5 4/5 1/5 1/5 1/5 1/5 - 2 3 + 3 + 2 2 3 - 2 3 + 2 sqrt(4 - 3 ) = ---------------------------------------------------. 5 And, of course, these can only give pentanomials. --rwg ALGORISMIC MICROGLIAS