A certain perfect square has exactly 4 digits (it is an integer between 1,000 and 9,999). The positive square root must have how many digits?
E) Cannot be determined from the given information.
The correct answer is H.
A good approach to answering this question is to look first at the high end of the interval. You know that 100^2 = 10,000, which is not in the interval. Therefore, the largest perfect square in the interval must be 99, which has 2 digits. Eliminate answer choices A and B.
Use common sense and trial and error to find the smallest perfect square in the interval:
Start with 30 (an easy number to work with): 30^2 = 900, which is not in the interval.
Try 31: 31^2 = 961, which is not in the interval. Try 32: 32^2 = 1,024, which is in the interval.
So, the perfect squares range from 32 to 99, which means that the positive square root of any number in the given interval must have 2 digits.
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