This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the properties of perfect squares. A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because 3^2 = 9. The last digit of a perfect square can only be 0, 1, 4, 5, 6, or 9. Therefore, any number ending in 2, 3, 7, or 8 cannot be a perfect square. Step 2: Examine the last digit of each given number. (i) 2032: The last digit is 2. (ii) 2048: The last digit is 8. (iii) 1027: The last digit is 7. (iv) 1089: The last digit is 9. Step 3: Identify numbers that are not perfect squares based on their last digit. Since 2032 ends in 2, it is not* a perfect square. Since 2048 ends in 8, it is not* a perfect square. Since 1027 ends in 7, it is not* a perfect square. Step 4: Verify numbers that could be perfect squares. 1089 ends in 9, so it could* be a perfect square. To check, we can find its square root. We know that 30^2 = 900 and 44^2 = 1936. Since 1089 ends in 9, its square root must end in 3 or 7. Let's try 33^2: 33^2 = 33 × 33 = 1089 Thus, 1089 is a perfect square. Step 5: Conclude which numbers are not perfect squares. Based on the analysis, the numbers that are not perfect squares are 2032, 2048, and 1027. The numbers that are not perfect squares are: (i) 2032* (ii) 2048* (iii) 1027* Send me the next one 📸