`sqrt(?)+22=sqrt(2601)`

Options

A. `sqrt(841)`
B. `(841)^(2)`
C. `sqrt(22)`
D. None of these

Explanation

To solve the equation \( \sqrt{?} + 22 = \sqrt{2601} \), we will follow these steps:

### Step 1: Rewrite the equation
Let \( ? = X \). Therefore, we can rewrite the equation as:
\[ \sqrt{X} + 22 = \sqrt{2601} \]

### Step 2: Calculate \( \sqrt{2601} \)
Next, we need to find the value of \( \sqrt{2601} \). We can check if 2601 is a perfect square:
\[ 2601 = 51 \times 51 \]
Thus,
\[ \sqrt{2601} = 51 \]

### Step 3: Substitute back into the equation
Now we substitute \( \sqrt{2601} \) back into the equation:
\[ \sqrt{X} + 22 = 51 \]

### Step 4: Isolate \( \sqrt{X} \)
To isolate \( \sqrt{X} \), we subtract 22 from both sides:
\[ \sqrt{X} = 51 - 22 \]
Calculating the right side gives:
\[ \sqrt{X} = 29 \]

### Step 5: Square both sides
To find \( X \), we square both sides of the equation:
\[ X = 29^2 \]
Calculating \( 29^2 \):
\[ X = 841 \]

### Final Answer
Thus, the value of \( ? \) is:
\[ \boxed{841} \]

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