What is the value od `53^2`?

Options

A. 2509
B. 2849
C. 2809
D. 2909

Answer

To find the value of \( 53^2 \), we can use the identity for the square of a binomial. The identity states that:

\[ (a + b)^2 = a^2 + 2ab + b^2 \]

In this case, we can represent \( 53 \) as \( 50 + 3 \). Therefore, we can rewrite \( 53^2 \) as:

\[ (50 + 3)^2 \]

Now, we can apply the identity:

1. Identify \( a \) and \( b \):
- \( a = 50 \)
- \( b = 3 \)

2. Substitute into the identity:
\[ (50 + 3)^2 = 50^2 + 2 \cdot 50 \cdot 3 + 3^2 \]

3. Calculate each term:
- \( 50^2 = 2500 \)
- \( 2 \cdot 50 \cdot 3 = 300 \)
- \( 3^2 = 9 \)

4. Now, combine all the terms:
\[ 53^2 = 2500 + 300 + 9 \]

5. Perform the addition:
- First, add \( 2500 + 300 = 2800 \)
- Then, add \( 2800 + 9 = 2809 \)

Thus, the value of \( 53^2 \) is:

\[ \boxed{2809} \]