We are familiar with this pattern: 1,4,9,16,25,36,49,64,81,100…

Start with square of 11 ==>          121,144,169,196,225,256,289,324,361,400…

Ending digits for 1st set :  1,4,6,9,6,5,6,9,4,1,0

Ending digits for 2nd set: 1,4,6,9,6,5,6,9,4,1,0

This pattern repeats itself.

So, numbers ending with 2,3,7,8 cannot be perfect squares!