Find the least number which must be added to 6412 to make a perfect square 

To find the least number that must be added to 6412 to make it a perfect square, follow these steps:

1. **Estimate the nearest square root of 6412:**
   Calculate the approximate square root of 6412. 

2. **Identify the nearest integers around the square root:**
   Find the nearest whole numbers less than and greater than the square root of 6412.

3. **Calculate the squares of these integers:**
   Compute the squares of these two integers to determine the closest perfect squares above and below 6412.

4. **Subtract 6412 from the nearest higher perfect square:**
   The difference between 6412 and the nearest higher perfect square is the least number that must be added.

Let’s calculate these steps:

1. **Approximate Square Root:**
   \[
   \sqrt{6412} \approx 80.1
   \]

2. **Nearest Whole Numbers:**
   The integers around 80.1 are 80 and 81.

3. **Perfect Squares:**
   - \(80^2 = 6400\)
   - \(81^2 = 6561\)

4. **Find the Difference:**
   - \(6561 - 6412 = 149\)

Therefore, the least number that must be added to 6412 to make it a perfect square is **149**.

Would you like further details or have any questions? 

Here are some related questions:
1. What is a perfect square and how is it defined?
2. How do you find the nearest perfect square of a number?
3. What is the process to determine whether a number is a perfect square?
4. How can you calculate square roots without a calculator?
5. What other ways can be used to approximate square roots?

**Tip:** Always double-check calculations when dealing with approximations or manual square root estimations to ensure accuracy!

Find the least number which must be added to 6412 to make a perfect square

Learn how to determine the least number that must be added to 6412 to make it a perfect square. This problem explores concepts like square roots, perfect squares, and approximation methods, suitable for students in Grades 7-10.

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