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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
We need to find all perfect squares between 1 and 250. A perfect square is a number that can be expressed as the product of an integer with itself.
Step 3:: Determine the Range of Possible Integers
\sqrt{250} \approx 15.81
We'll start by finding the largest integer whose square is less than or equal to 250. This means we'll check squares of integers from 1 to 15.
Step 4:: List the Perfect Squares
15^{2} = 225
Let's systematically list out the squares:
Final Answer
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
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