66If you divide a perfect square by 100, there are only 23 possible remainders:
0, 1, 4, 9, 16, 21, 24, 25, 29, 36,
41, 44, 49, 56, 61, 64, 69, 76, 81, 84,
89, 96, 96
It is easily seen that if the tens place is 7, the units place can only be 6.
A square has tens digit 7.Find its units digit
I want to learn the basic concept of this question more than just the answer :-)
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2 Answers
66
341since the units digit of a perfect can only be 0,1,4,5, 6 or 9, the last two digits of the number are possibly 70,71,74,75,76 or 79.
We know that every perfect square is of the form 4k or 4k+1.
Of the given possibilities only a number that ends with 76 satisfies the criteria. Hence, the units digit of the number is 6.