The teacher clapped her hands to disperse the students to the playground.

disperse 是动词，由前缀 dis-（表示"分开、分散"）和词根 -perse（来自拉丁语 spargere，意为"撒播、散布"）组成，意思是"使分散、散开"。在句中指老师通过拍手让学生们分散到操场各处。