When `73^2` is subtracted from the square of a number, the answer that is obtained is 5280. What is the number?

Options

A. 97
B. 103
C. 99
D. 101

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Set up the equation
We are given that when \( 73^2 \) is subtracted from the square of a number \( x \), the result is 5280. We can express this mathematically as:
\[ x^2 - 73^2 = 5280 \]

### Step 2: Calculate \( 73^2 \)
Now, we need to calculate \( 73^2 \):
\[ 73^2 = 5329 \]

### Step 3: Substitute \( 73^2 \) into the equation
Now we can substitute \( 5329 \) back into our equation:
\[ x^2 - 5329 = 5280 \]

### Step 4: Solve for \( x^2 \)
Next, we add \( 5329 \) to both sides of the equation to isolate \( x^2 \):
\[ x^2 = 5280 + 5329 \]

### Step 5: Perform the addition
Now we perform the addition:
\[ x^2 = 10609 \]

### Step 6: Take the square root
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{10609} \]

### Step 7: Calculate the square root
Now we calculate \( \sqrt{10609} \):
\[ x = 103 \]

### Conclusion
Thus, the number is:
\[ \boxed{103} \]