Find the square of 211

Answer

To find the square of 211, we can use the algebraic identity for the square of a binomial. The identity states that:

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

In this case, we can express 211 as \(200 + 11\). Thus, we can set \(a = 200\) and \(b = 11\).

Now, let's apply the identity step by step:

1. **Identify \(a\) and \(b\)**:
- Let \(a = 200\)
- Let \(b = 11\)

2. **Use the identity**:
\[ (a + b)^2 = a^2 + b^2 + 2ab \]
Substituting \(a\) and \(b\):
\[ (200 + 11)^2 = 200^2 + 11^2 + 2 \cdot 200 \cdot 11 \]

3. **Calculate \(a^2\)**:
\[ 200^2 = 40000 \]

4. **Calculate \(b^2\)**:
\[ 11^2 = 121 \]

5. **Calculate \(2ab\)**:
\[ 2 \cdot 200 \cdot 11 = 4400 \]

6. **Combine all the results**:
\[ 211^2 = 40000 + 121 + 4400 \]

7. **Perform the addition**:
\[ 40000 + 4400 = 44400 \]
\[ 44400 + 121 = 44521 \]

Thus, the square of 211 is:

\[ \boxed{44521} \]