Find the approx value of:- 15.33^2 - 12.94^2 + 22.06^2 - 35.65 = ?

Options

A. a. 720
B. b. 505
C. c. 402
D. c. 600

Answer

To find the approximate value of the expression \( 15.33^2 - 12.94^2 + 22.06^2 - 35.65 \), we can follow these steps:

### Step 1: Calculate \( 15.33^2 \)
Using the approximation:
\[ 15.33^2 \approx (15.3)^2 = 234.09 \]

### Step 2: Calculate \( 12.94^2 \)
Using the approximation:
\[ 12.94^2 \approx (12.9)^2 = 166.41 \]

### Step 3: Calculate \( 22.06^2 \)
Using the approximation:
\[ 22.06^2 \approx (22.1)^2 = 488.41 \]

### Step 4: Combine the results
Now we substitute the approximated values into the expression:
\[ 15.33^2 - 12.94^2 + 22.06^2 - 35.65 \approx 234.09 - 166.41 + 488.41 - 35.65 \]

### Step 5: Perform the calculations step by step
1. Calculate \( 234.09 - 166.41 \):
\[ 234.09 - 166.41 = 67.68 \]

2. Add \( 488.41 \):
\[ 67.68 + 488.41 = 556.09 \]

3. Subtract \( 35.65 \):
\[ 556.09 - 35.65 = 520.44 \]

### Final Result
Thus, the approximate value of the expression is:
\[ \approx 520.44 \]