Find the values of the following by using suitable identity:
`(55)^(2)`

Answer

To find the value of \( (55)^2 \) using a suitable identity, we can use the identity for the square of a binomial:

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

In this case, we can express \( 55 \) as \( 50 + 5 \). Here, \( a = 50 \) and \( b = 5 \).

Now, we can apply the identity:

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

2. **Calculate \( b^2 \)**:
\[ b^2 = (5)^2 = 25 \]

3. **Calculate \( 2ab \)**:
\[ 2ab = 2 \times 50 \times 5 = 500 \]

4. **Combine all parts**:
\[ (50 + 5)^2 = a^2 + 2ab + b^2 = 2500 + 500 + 25 \]

5. **Final calculation**:
\[ 2500 + 500 + 25 = 3025 \]

Thus, the value of \( (55)^2 \) is \( 3025 \).