We are tasked with finding the least number that must be added to 1876 to get a perfect square. Let's go through the steps:

Step 1: Find the square root of 1876

First, let's find the approximate square root of 1876: $\sqrt{1876} \approx 43.3$ This means the next perfect square is the square of 44 (since 43.3 rounds up to 44).

Step 2: Square the next integer

We calculate the square of 44: $44^2 = 1936$

Step 3: Find the difference

Now, subtract 1876 from 1936 to determine the least number to add: $1936 - 1876 = 60$

Step 4: Conclusion

The least number that must be added to 1876 to make it a perfect square is 60. The square root of the resulting number (1936) is 44.

Final Answer:

• The least number to be added: 60
• The square root of the resulting perfect square: 44

Do you want more details or have any questions?

Here are 5 related questions:

1. What is the smallest number that can be added to 2000 to make it a perfect square?
2. How can we find the nearest perfect square of any given number?
3. How do you compute square roots manually for large numbers?
4. What is the largest number that must be subtracted from 1936 to still have a perfect square?
5. Can you find a formula to estimate how close a number is to being a perfect square?

Tip: To approximate square roots quickly, you can use estimation by finding nearby perfect squares and narrowing down with a decimal.