To solve the problem, let's follow these steps:
1. Identify the largest perfect square less than or equal to 1255:
- A perfect square is a number that can be expressed as the square of an integer. To find the largest perfect square less than or equal to 1255, we look for an integer \( n \) such that \( n^2 \leq 1255 \).
- Through our calculations, we find that the largest perfect square less than or equal to 1255 is 1225 (since \( 35^2 = 1225 \)).
2. Calculate the number that must be subtracted from 1255 to get 1225:
- To make 1255 a perfect square, we subtract the difference between 1255 and the largest perfect square we found.
- The number to be subtracted is \( 1255 - 1225 = 30 \).
3. Find the square root of the resulting perfect square:
- We have now determined that the largest perfect square less than or equal to 1255 is 1225.
- The square root of 1225 is \( \sqrt{1225} = 35 \).
Summarizing the results:
- The largest perfect square less than or equal to 1255 is 1225.
- The number that must be subtracted from 1255 to make it a perfect square is 30.
- The square root of the perfect square obtained (1225) is 35.
