`(32.05)^(2)-(18.9)^(2)-(11.9)^(2)=?`

Options

A. 670
B. 530
C. 420
D. 780

Explanation

To solve the equation `(32.05)^(2)-(18.9)^(2)-(11.9)^(2)` using approximation, we can follow these steps:

### Step 1: Round Off the Numbers
- Round 32.05 to the nearest whole number, which is 32.
- Round 18.9 to the nearest whole number, which is 19.
- Round 11.9 to the nearest whole number, which is 12.

### Step 2: Rewrite the Expression
Now, we can rewrite the expression using the rounded numbers:
\[ (32)^{2} - (19)^{2} - (12)^{2} \]

### Step 3: Calculate Each Square
- Calculate \(32^2\):
\[ 32^2 = 1024 \]
- Calculate \(19^2\):
\[ 19^2 = 361 \]
- Calculate \(12^2\):
\[ 12^2 = 144 \]

### Step 4: Substitute the Values
Now substitute these values back into the expression:
\[ 1024 - 361 - 144 \]

### Step 5: Perform the Subtraction
First, subtract \(361\) from \(1024\):
\[ 1024 - 361 = 663 \]
Next, subtract \(144\) from \(663\):
\[ 663 - 144 = 519 \]

### Step 6: Conclusion
The approximate value of the expression is \(519\). Since we are looking for the closest approximation, we can round \(519\) to \(530\) as the final answer.

Thus, the final answer is:
\[ \text{Approximately } 530 \]

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