In imaginary numbers can you multiply two radicals that have negative values under them that do not square to whole numbers

Yes, you can; based on the inherent assumption that the "two radicals that have negative values" are, in fact, "imaginary numbers" .

Take, for example, the commonly known "imaginary number":  "i" ;  which represents the "imaginary number" ;  " √-1 " .

Since:  "i = √-1" ; 

Note that:   " i² = (√-1)² = √-1 * √-1 = √(-1*-1) = √1 = 1 .

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