What is the value of `47^2`?

Options

A. 2249
B. 2349
C. 2209
D. 2149

Answer

To find the value of \( 47^2 \), we can use the identity for the square of a binomial, which states that:

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

In this case, we can express \( 47 \) as \( 50 - 3 \). Here, \( a = 50 \) and \( b = 3 \).

Now, we can apply the identity:

1. **Calculate \( a^2 \)**:
\[ a^2 = 50^2 = 2500 \]

2. **Calculate \( b^2 \)**:
\[ b^2 = 3^2 = 9 \]

3. **Calculate \( 2ab \)**:
\[ 2ab = 2 \times 50 \times 3 = 300 \]

4. **Combine the results using the identity**:
\[ 47^2 = (50 - 3)^2 = 50^2 - 2 \times 50 \times 3 + 3^2 \]
\[ = 2500 - 300 + 9 \]

5. **Perform the arithmetic**:
\[ 2500 - 300 = 2200 \]
\[ 2200 + 9 = 2209 \]

Thus, the value of \( 47^2 \) is \( 2209 \).