Find the values of the following by using suitable identity:
`52.5xx47.5`

Answer

To find the value of \( 52.5 \times 47.5 \) using a suitable identity, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers**: We have \( 52.5 \) and \( 47.5 \). We can express these numbers in a form that is easier to work with. Notice that both numbers are close to \( 50 \).

2. **Rewrite the Numbers**:
- \( 52.5 \) can be rewritten as \( 50 + 2.5 \).
- \( 47.5 \) can be rewritten as \( 50 - 2.5 \).

3. **Use the Identity**: We can use the identity for the product of a sum and a difference:
\[ (a + b)(a - b) = a^2 - b^2 \]
Here, let \( a = 50 \) and \( b = 2.5 \).

4. **Apply the Identity**:
\[ 52.5 \times 47.5 = (50 + 2.5)(50 - 2.5) = 50^2 - (2.5)^2 \]

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

6. **Calculate \( (2.5)^2 \)**:
\[ (2.5)^2 = 6.25 \]

7. **Subtract the Values**:
\[ 2500 - 6.25 = 2493.75 \]

### Final Answer:
Thus, the value of \( 52.5 \times 47.5 \) is \( 2493.75 \).

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