Help me please??

Dear student,

these both belong to the class insecta of phylum arthropoda so there are many similarities between them but a few obvious differences are :

1. grasshopper is green and cockroaches are mid brown to reddish brown in colour.
2. grasshopper cannot fly while cockroaches can 
3. Cockroaches are vectors of many diseases while grasshoppers do not cause any diseases as such.
4. Cockroaches have a comparatively hard exoskeleton than grasshopper.
5. cockroaches have quite long antennae which are sensitive but grasshoppers have relatively short antennae.

Regards.