What least number must be added to 5607 to make the sum a perfect square ? Fnd this perfect square and its square root.

Answer

To solve the problem of finding the least number that must be added to 5607 to make it a perfect square, we can follow these steps:

### Step 1: Find the nearest perfect square greater than 5607.
To do this, we first need to determine the square root of 5607.

1. **Calculate the approximate square root of 5607.**
- We can find the square root by estimating. The square root of 5600 is approximately 74.83, so we can round it to 75 for our calculations.

### Step 2: Calculate the perfect squares around this estimate.
2. **Calculate the squares of 75 and 76.**
- \(75^2 = 5625\)
- \(76^2 = 5776\)

### Step 3: Identify the nearest perfect square.
3. **Determine which perfect square is closest to 5607.**
- The nearest perfect square greater than 5607 is \(75^2 = 5625\).

### Step 4: Calculate the difference.
4. **Find the difference between 5625 and 5607.**
- \(5625 - 5607 = 18\)

### Step 5: Conclusion.
5. **State the least number to be added and the perfect square.**
- The least number that must be added to 5607 to make it a perfect square is **18**.
- The perfect square is **5625** and its square root is **75**.

### Summary of the Solution:
- The least number to be added: **18**
- The perfect square: **5625**
- The square root of the perfect square: **75**