Choosing a number related to a given number in the same manner as the two numbers of another given pair are related to each other
82 : 9 :: 26 : ?

Options

A. 5
B. 6
C. 4
D. 9

Explanation

To solve the analogy problem 82 : 9 :: 26 : ?, we need to determine the relationship between the numbers in the first pair (82 and 9) and then apply the same relationship to the second pair (26 and ?).

### Step 1: Analyze the first pair (82 and 9)
We start with the first pair of numbers: 82 and 9.

To find the relationship, we can express 82 in terms of 9:
- We notice that \(9^2 = 81\).
- If we add 1 to \(81\), we get \(82\).

Thus, the relationship can be expressed as:
\[ 82 = 9^2 + 1 \]

### Step 2: Apply the same relationship to the second pair (26 and ?)
Now, we need to find the number that relates to 26 in the same way that 9 relates to 82.

Let’s denote this unknown number as \(x\). According to the established relationship:
\[ 26 = x^2 + 1 \]

### Step 3: Solve for x
To find \(x\), we rearrange the equation:
\[ x^2 = 26 - 1 \]
\[ x^2 = 25 \]

Now, we take the square root of both sides:
\[ x = \sqrt{25} \]
\[ x = 5 \]

### Conclusion
Thus, the number that relates to 26 in the same manner as 9 relates to 82 is:
\[ ? = 5 \]

So, the final answer is:
**5**