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 start with the information given:

1. **Understanding the Problem**: We need to find a number \( x \) such that when \( 73^2 \) is subtracted from \( x^2 \), the result is 5280.

2. **Setting Up the Equation**: We can express this mathematically as:
\[ x^2 - 73^2 = 5280 \]

3. **Calculating \( 73^2 \)**: First, we need to calculate \( 73^2 \):
\[ 73^2 = 5329 \]

4. **Substituting Back into the Equation**: Now we substitute \( 73^2 \) back into our equation:
\[ x^2 - 5329 = 5280 \]

5. **Isolating \( x^2 \)**: Next, we add \( 5329 \) to both sides of the equation to isolate \( x^2 \):
\[ x^2 = 5280 + 5329 \]
\[ x^2 = 10609 \]

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

7. **Calculating the Square Root**: Now we calculate \( \sqrt{10609} \):
\[ x = 103 \]

Thus, the number we are looking for is **103**.