If `(41)^2` is added to the square of a number the answer, so obtained is 7457. What is the number?

Options

A. 76
B. 63
C. 81
D. 82

Answer

To solve the problem, we need to find the number \( x \) such that when the square of 41 is added to the square of \( x \), the result is 7457.

Let's break this down step by step:

### Step 1: Write the equation based on the problem statement.
We start with the equation:
\[ 41^2 + x^2 = 7457 \]

### Step 2: Calculate \( 41^2 \).
Next, we need to calculate \( 41^2 \):
\[ 41^2 = 41 \times 41 = 1681 \]

### Step 3: Substitute \( 41^2 \) into the equation.
Now we substitute \( 41^2 \) back into the equation:
\[ 1681 + x^2 = 7457 \]

### Step 4: Isolate \( x^2 \).
To find \( x^2 \), we subtract 1681 from both sides:
\[ x^2 = 7457 - 1681 \]

### Step 5: Perform the subtraction.
Now, we calculate the right side:
\[ 7457 - 1681 = 5776 \]

### Step 6: Take the square root of both sides.
Now we take the square root to find \( x \):
\[ x = \sqrt{5776} \]

### Step 7: Calculate \( \sqrt{5776} \).
Calculating the square root:
\[ \sqrt{5776} = 76 \]

### Final Answer:
Thus, the number \( x \) is:
\[ \boxed{76} \]