What approximate value will come in place of question mark(?) in the questions given below?
5670 `div 380xx (21)^2,= ?`

Options

A. 6800
B. 6700
C. 6580
D. 6600

Answer

To solve the problem \( 5670 \div (380 \times (21)^2) = ? \), we will follow these steps:

### Step 1: Calculate \( (21)^2 \)
First, we need to calculate \( 21^2 \):
\[ 21^2 = 441 \]

**Hint:** Remember that squaring a number means multiplying it by itself.

### Step 2: Multiply \( 380 \) by \( 441 \)
Next, we multiply \( 380 \) by \( 441 \):
\[ 380 \times 441 \]
To simplify the multiplication, we can break it down:
\[ 380 \times 441 = 380 \times (400 + 41) = (380 \times 400) + (380 \times 41) \]
Calculating each part:
\[ 380 \times 400 = 152000 \]
\[ 380 \times 41 = 15580 \]
Now, adding these two results:
\[ 152000 + 15580 = 167580 \]

**Hint:** Breaking down multiplication into smaller parts can make calculations easier.

### Step 3: Divide \( 5670 \) by \( 167580 \)
Now, we will divide \( 5670 \) by \( 167580 \):
\[ 5670 \div 167580 \]
Calculating this gives:
\[ 5670 \div 167580 \approx 0.0339 \]

**Hint:** When dividing, you can use a calculator for quick results, especially with large numbers.

### Step 4: Multiply the result by \( 441 \)
Next, we multiply the result by \( 441 \):
\[ 0.0339 \times 441 \approx 14.92 \]

**Hint:** Multiplying decimals can be tricky; ensure you keep track of the decimal places.

### Step 5: Final Calculation
Now, we round \( 14.92 \) to the nearest whole number and multiply by \( 441 \):
\[ 14.92 \times 441 \approx 6579.72 \]

### Conclusion
The approximate value that comes in place of the question mark is:
\[ \approx 6580 \]

**Final Answer:** The answer is \( 6580 \) (Option C).