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A perfect square number can never have the digit ______ at the units' place.
1
9
4
8
8
Remember the sequence of unit digits of squares from 0 to 9: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1. The digits 2, 3, 7, and 8 are never present in this list.
The question asks for the digit that a perfect square number can never have at the units' place.
n2≡{0,1,4,5,6,9}(mod10)
Remember the sequence of unit digits of squares from 0 to 9: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1. The digits 2, 3, 7, and 8 are never present in this list.
Many students try to check numbers manually instead of recalling the property of the units digit of perfect squares.
List squares of digits 0-9
Calculate the squares of all digits from 0 to 9 and identify their units' digit.
02=0,12=1,22=4,32=9,42=16,52=25,62=36,72=49,82=64,92=81
Identify unit digits
The possible unit digits for any perfect square are 0,1,4,5,6,9.
U∈{0,1,4,5,6,9}
Check the options
Compare the provided options (1, 9, 4, 8) against the set of possible unit digits. The digit 8 is not in the set.
8∈/{0,1,4,5,6,9}
D is correct because 8 can never be the unit digit of a perfect square number.
This property is extremely useful for 'Option Elimination' in competitive exams when checking if a large number could be a perfect square.
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