Question

Some properties of square and square root:
i) Complete square of a number is possible if its last digit is 0,1,4,5,6 & 9.
If last digit of a no is 2,3,7,8 then complete square root of this number is not possible
ii) If last digit of a number is 1 ,then last digit of its complete square is either 1 or 9.
iii)if last digit of a number is 4, then last digit of its complete square is either 2 or 8.
iv) if last digit of a number is 5 or 0 ,then last digit of its complete square root is either 5 or 0
v) if last digit of a number is 6 ,then last digit of its complete square root is either 4 or 6.
vi) If last digit of a number is 9 then last digit of its complete square root is either 3 or 7

Give 2 examples for each and every property.
if possible in table form

Answer 1

1) last digit zero :- 100=(10)² , (400)² =(20)²
last digit 1 :- 121 =(11)² , 81 =(9)²
last digit 4 :- 64 =(8)² , 484=(22)²
last digit 5:- 25 =(5)² , 225=(15)²
last digit 6 :- 36=(6)² , (256)² =(16)²
last digit 9 :- 49 =(7)² , 529=(23)²

now if
last digit 2 :- 2=(1.414.....)², 12 =(3.4...)²
last digit 3 :- 3 =(1.732...)² , 13 =(3.6...)²
last digit 7 :- 7=(2.6...)² , 17 =(4.1...)²
last digit 8 :- 8 =(2.8...)² , 18=(4.2..)²

2)if last digit 1 then,
121 = (11)²
81 =(9)²

3) if last digit 4
144 = (12)²
324 =(18)²

4) if last digit 5
225 = (15)²
625 =(25)²

last digit zero
100 = (10)²
400=(20)²

5) if last digit 6
256 =(16)²
196 =(14)²

6) if last digit 9

529 =(23)²
289 =(17)²