Find the least number which must be added to 8400 to obtain a perfect square. Find this perfect square and its square root.

Answer

To solve the problem of finding the least number that must be added to 8400 to obtain a perfect square, we will follow these steps:

### Step 1: Find the square root of 8400
We start by estimating the square root of 8400. The nearest perfect squares are:
- \( 90^2 = 8100 \)
- \( 91^2 = 8281 \)
- \( 92^2 = 8464 \)

Since \( 8400 \) is between \( 91^2 \) and \( 92^2 \), we can conclude that the square root of \( 8400 \) is between \( 91 \) and \( 92 \).

### Step 2: Identify the next perfect square
The next perfect square after \( 8400 \) is \( 92^2 = 8464 \).

### Step 3: Calculate the difference
Now, we need to find the difference between \( 8464 \) and \( 8400 \):
\[ 8464 - 8400 = 64 \]

### Step 4: Conclusion
The least number that must be added to \( 8400 \) to obtain a perfect square is \( 64 \). The perfect square we obtain is \( 8464 \), and its square root is \( 92 \).

### Summary of the solution:
- The least number to be added: **64**
- The perfect square: **8464**
- The square root of the perfect square: **92**