Find the least number that must be added to 1500 so as to get a perfect square root of the perfect square
The Correct Answer and Explanation is:
To solve this problem, we need to find the least number that must be added to 1500 to make the result a perfect square.
Step 1: Understand the problem
We are given the number 1500 and asked to find the smallest number that can be added to it so that the sum is a perfect square. A perfect square is a number that can be expressed as the square of an integer.
Step 2: Find the square root of 1500
Let’s estimate the square root of 1500.1500≈38.73\sqrt{1500} \approx 38.731500≈38.73
The closest integer greater than 38.73 is 39.
Now we square 39:392=152139^2 = 1521392=1521
So the next perfect square after 1500 is 1521.
Step 3: Find the difference
1521−1500=211521 – 1500 = 211521−1500=21
Final Answer: 21
Explanation
To determine the least number that must be added to 1500 to create a perfect square, we begin by identifying what a perfect square is. A perfect square is an integer that is the square of another integer. Examples include 1, 4, 9, 16, 25 and so on. These numbers are special because their square roots are whole numbers.
Given the number 1500, we are looking for the smallest number we can add so that the result is a perfect square. We start by estimating the square root of 1500. The square root of 1500 lies between two perfect squares. Since 382=144438^2 = 1444382=1444 and 392=152139^2 = 1521392=1521, the square root of 1500 must lie between 38 and 39. Specifically, it is about 38.73. Because the result must be a perfect square, we move to the next whole number, 39, and square it.
When we square 39, we get 1521. This is the smallest perfect square greater than 1500. To find out how much we need to add to 1500 to reach 1521, we subtract 1500 from 1521. This gives us:1521−1500=211521 – 1500 = 211521−1500=21
Therefore, the least number that must be added to 1500 to make the result a perfect square is 21. This approach ensures we find the smallest possible addition required to achieve a perfect square, making the method efficient and accurate.
