The smallest number that should be added to 8212 to obtain a perfect square is:

Options

A. 123
B. 69
C. 54
D. 112

Answer

To find the smallest number that should be added to 8212 to obtain a perfect square, we can follow these steps:

### Step 1: Identify the nearest perfect square
First, we need to find the nearest perfect square greater than 8212. We can do this by taking the square root of 8212.

\[ \sqrt{8212} \approx 90.7 \]

### Step 2: Determine the next whole number
Since we need a perfect square, we round up to the next whole number, which is 91.

### Step 3: Calculate the perfect square
Now, we calculate the perfect square of 91:

\[ 91^2 = 8281 \]

### Step 4: Find the difference
Next, we find the difference between 8281 and 8212 to determine how much we need to add:

\[ 8281 - 8212 = 69 \]

### Conclusion
Thus, the smallest number that should be added to 8212 to obtain a perfect square is **69**.

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