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: Recall the properties of perfect squares. A perfect square can only end in the digits 0, 1, 4, 5, 6, or 9. Numbers ending in 2, 3, 7, or 8 are never perfect squares. Step 2: Examine the one's digit of each given number. (i)* 153: The one's digit is 3. (ii)* 257: The one's digit is 7. (iii)* 408: The one's digit is 8. (iv)* 441: The one's digit is 1. Step 3: Identify the numbers that are surely not perfect squares based on their one's digit. Numbers ending in 3, 7, or 8 are not perfect squares. 153 ends in 3, so it is surely not a perfect square. 257 ends in 7, so it is surely not a perfect square. 408 ends in 8, so it is surely not a perfect square. 441 ends in 1, which means it could* be a perfect square (in fact, 21^2 = 441). The numbers which are surely not perfect squares are 153, 257, and 408. Last free one today — make it count tomorrow, or type /upgrade for unlimited.