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Cassini
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Are all of the Fs real? If so, try this:

Assuming[{F11, F12, F13, F21, F22, F24, F33, F35, F44, F45, F53, F54, F55} \[Element] Reals, MatrixPower[Ftemp, 1/2]] 

You'll get an answer, but it'll be ugly...

David Skulsky
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