What is the leat natural number that should be added to the result of `88xx89`, so that the sum obtained is a perfect square?

Options

A. 1
B. 8
C. 88
D. 89

Answer

To find the least natural number that should be added to the result of \(88 \times 89\) so that the sum obtained is a perfect square, we can follow these steps:

### Step 1: Calculate \(88 \times 89\)

First, we need to calculate the product:

\[ 88 \times 89 = 7792 \]

### Step 2: Identify the nearest perfect squares

Next, we need to find the perfect squares that are closest to \(7792\). The perfect squares around this number can be calculated by finding the square roots of numbers close to \(7792\).

Calculating the square root:

\[ \sqrt{7792} \approx 88.3 \]

This means the nearest perfect squares are \(88^2\) and \(89^2\).

Calculating these perfect squares:

\[ 88^2 = 7744 \]
\[ 89^2 = 7921 \]

### Step 3: Determine which perfect square is greater

Since \(7792\) is between \(7744\) and \(7921\), we see that \(7921\) is the next perfect square greater than \(7792\).

### Step 4: Calculate the difference to find the least natural number

Now, we need to find the least natural number \(k\) that should be added to \(7792\) to reach \(7921\):

\[ k = 7921 - 7792 \]

Calculating this gives:

\[ k = 129 \]

### Conclusion

Thus, the least natural number that should be added to \(88 \times 89\) to make it a perfect square is:

\[ \boxed{129} \]

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