Answer: One answer would probably be "frequently and well", but an easier way to handle weeds is to prevent them from growing in the first place by using a thick layer of mulch. If the mulch is refreshed periodically, this will prevent weeds from germinating in it. Larger weeds can be pulled individually or, in some cases, perennial weeds can be controlled by cutting them off repeatedly at the ground until their root reserves become exhausted. In summer when the asparagus has stopped growing new shoots, you can also use several layers of newspaper beneath the mulch to help smother any persistent weeds.
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