A, B, and C each can be any digit 0 through 9, possibly the same. The seven-digit whole number: 20ABC01 is a perfect square. What is the middle digit, B?
A.1 B.3 C.5 D.7 E. 9
The smallest possible number 20ABC01 could be, (even
if it weren't necessarily a perfect square) is 2000001
and the largest it could be would be 2099901. The
square roots of those are 1414.213916 and 1449.103516
Therefore the first two digits of the square root of 20ABC01
must be 14, and it is between 1414 and 1449
Looking at a list of squares of the first 100 integers,
we see that the only perfect squares that end in 01 are
squares of numbers that end in 01, 49, 51, and 99
The only square root 20ABC01 could have and be in that
range would be 1449, and is 2099601.
So the middle digit is 9, choice E
Edwin