Question: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? A) 4 B) 3 C) 2 D) 1 E) Cannot be determined from the given information. Solution: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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