What is the smallest number that should be added to 520 to make it a perfect square?
The correct answer and explanation is:
To find the smallest number that should be added to 520 to make it a perfect square, we need to determine the closest perfect square greater than 520.
First, find the square root of 520: 520≈22.8\sqrt{520} \approx 22.8
The next whole number greater than 22.8 is 23. Now, we calculate the square of 23: 232=52923^2 = 529
The next perfect square is 529, and we need to determine how much should be added to 520 to reach 529. Subtract 520 from 529: 529−520=9529 – 520 = 9
Therefore, the smallest number that should be added to 520 to make it a perfect square is 9.
Explanation
A perfect square is a number that can be expressed as the square of an integer. The key to solving this problem is finding the closest perfect square greater than 520. To do this, we first take the square root of 520 and find that it is approximately 22.8. Since the square root is not an integer, 520 itself is not a perfect square.
The next step is to find the next integer, which is 23, and square it. The square of 23 is 529, which is the smallest perfect square greater than 520. By subtracting 520 from 529, we determine that 9 is the smallest number that must be added to 520 to make it a perfect square.
This method involves understanding the concept of square roots and knowing how to find the next perfect square above a given number. It is a straightforward approach to solving problems involving perfect squares.