On concept images and square roots

This paper discusses the consequences of the de¢nition of a concept not standing at the core of one’s image of that concept. It then zeros in on ffiffiffi pn, and takes the position that it is not enough for students to know the de¢nition of what ^pffiffiffi n means, but that they should also know some ffiffiffi method which would enable them to compute pn, although carrying out the actual computation is not important. Several relatively known and unknown methods to compute ^pffiffiffi n are then discussed.