Why is the nos form of 'jugar', spelt 'jugamos' and not 'juegamos'

The nos form of 'jugar' is spelt 'jugamos' and not 'juegamos' because it is a radical changing verb. This means that the stem of the verb does not stay the same as it would with regular verbs, such as comer or beber. With radical changing verbs, the stems are the same as the infinitive of the verb, in this case jugar, for the nos and vos forms of the verb. However, for the yo, tu, él/Ella and ellos/ellas, the stem is slightly different, in this case with u changing to ue.
There are some key radical changing verbs to learn that will carry you through with your Spanish studies, such as:
Empezar (e becomes ie, e.g. empiezo, empiezas, empieza, empezamos, empezáis, empiezan)Dormir (o becomes ue, e.g. duermo, duermes, duerme, dormimos, dormís, duermen)Querer (ue becomes ui, e.g. quiero, quieres, quiere, queremos, queréis, quieren)Pensar (e becomes ie, e.g. pienso, piensas, piensa, pensamos, pensais, piensan)Poder (o becomes ue, e.g. puedo, puedes, puede, podemos, podéis, pueden)