Which one of the following is the minimum value of the sum of two Integers whose product is 24?

Options

A. 25
B. 11
C. 8
D. 10

Answer

To find the minimum value of the sum of two integers whose product is 24, we can follow these steps:

### Step 1: Identify the pairs of integers whose product is 24.
We need to find pairs of integers (a, b) such that:
\[ a \times b = 24 \]

### Step 2: List the factor pairs of 24.
The factor pairs of 24 are:
1. (1, 24)
2. (2, 12)
3. (3, 8)
4. (4, 6)

### Step 3: Calculate the sum of each pair.
Now, we will calculate the sum of each pair:
1. For (1, 24):
\[ 1 + 24 = 25 \]
2. For (2, 12):
\[ 2 + 12 = 14 \]
3. For (3, 8):
\[ 3 + 8 = 11 \]
4. For (4, 6):
\[ 4 + 6 = 10 \]

### Step 4: Identify the minimum sum.
Now, we compare the sums calculated:
- 25
- 14
- 11
- 10

The minimum sum is:
\[ 10 \]

### Step 5: Conclusion
Thus, the minimum value of the sum of two integers whose product is 24 is:
\[ \boxed{10} \]