What is the least number to be added to 8200 to make it a perfect square?

Options

A. 81
B. 100
C. 264
D. 154

Answer

To find the least number to be added to 8200 to make it a perfect square, we can follow these steps:

### Step 1: Identify the square roots around 8200
First, we need to find the perfect squares that are closest to 8200. We can start by calculating the square root of 8200.

\[ \sqrt{8200} \approx 90.55 \]

### Step 2: Find the nearest whole numbers
The nearest whole numbers to 90.55 are 90 and 91. We will calculate their squares.

\[ 90^2 = 8100 \]
\[ 91^2 = 8281 \]

### Step 3: Determine which perfect square is greater than 8200
Since 8200 is between 8100 and 8281, we can see that the next perfect square greater than 8200 is \(91^2 = 8281\).

### Step 4: Calculate the difference
Now, we need to find out how much we need to add to 8200 to reach 8281.

\[ 8281 - 8200 = 81 \]

### Step 5: Conclusion
Thus, the least number that needs to be added to 8200 to make it a perfect square is:

\[ \text{Least number to be added} = 81 \]

### Final Answer
The least number to be added to 8200 to make it a perfect square is **81**.

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