solve(if, AB, = 12, and, AC, = 8, what, is, the, length, of, BC)

Assuming that we have a right triangle with hypotenuse AB  and legs AC and BC.....we have....

BC  =   sqrt   [ AB^2 - AC^2]   =   sqrt [ 12^2 - 8^2 ]   =  sqrt [ 144 - 64 ]  =  sqrt [80]  = 

sqrt [ 16 * 5 ]  =     sqrt [16] * sqrt [5]  =    4 sqrt [ 5]  

However.....it's also possible that BC is the hypotenuse and AB and AC are legs

In that case

BC  =  sqrt [ AB^2 + AC^2 ]  = sqrt [ 12^2 + 8^2 ]  =  sqrt [ 144 + 64 ]  =  sqrt [ 208 ]  =

sqrt [ 16 * 13 ]  =    sqrt [ 16]* sqrt [ 13 ]  =  4sqrt [ 13 ]