Let's break down the given question and solve it step by step:
Goal: To find the smallest number to be added to 8958 to make it a perfect square.
1. Understanding Perfect Squares: A perfect square is an integer that is the square of some other integer. For example, 1, 4, 9, 16, and 25 are perfect squares because they are 1[tex]\(^2\)[/tex], 2[tex]\(^2\)[/tex], 3[tex]\(^2\)[/tex], 4[tex]\(^2\)[/tex], and 5[tex]\(^2\)[/tex], respectively.
2. Explain the Process:
- To find the smallest number that should be added to 8958 to make it a perfect square, you need to determine the next perfect square after 8958.
- Then, subtract 8958 from this next perfect square to find the number that needs to be added.
3. Identification:
- The next perfect square after 8958 can be identified by finding the square root of 8958, rounding it up to the nearest whole number, and then squaring that number.
4. Outcome:
- Through a detailed calculation, it has been found that the smallest number to be added to 8958 to make it a perfect square is 67.
Thus, after adding 67 to 8958, we obtain a perfect square.
The correct answer is:
(b) 67
