To solve this problem step-by-step, we need to determine the smallest number that can be subtracted from 7230 to make it a perfect square and then find the square root of the resulting number.
1. Identify the initial number: We start with the number 7230.
2. Determine the smallest number to subtract: We need to find the smallest integer [tex]\( x \)[/tex] such that [tex]\( 7230 - x \)[/tex] is a perfect square.
3. Subtraction process: After evaluating various values of [tex]\( x \)[/tex], we find that subtracting 5 from 7230 results in a perfect square. Thus, the smallest number to be subtracted is 5.
4. Calculate the new number: Subtract 5 from 7230:
[tex]\[
7230 - 5 = 7225
\][/tex]
5. Verify that 7225 is a perfect square: We see that 7225 is indeed a perfect square.
6. Determine the square root: Now, we need to find the square root of 7225. The square root is 85, since:
[tex]\[
85 \times 85 = 7225
\][/tex]
Therefore, the least number which must be subtracted from 7230 to make it a perfect square is 5, and the square root of the resultant number 7225 is 85.
