What approximate value should come in place of the question mark (?) in the following questions ? (Note : You are not expected to calculate the exact value)
`sqrt(6354) xx 34.993 = ?`

Options

A. 3000
B. 2800
C. 2500
D. 2600

Answer

To find the approximate value of the expression \( \sqrt{6354} \times 34.993 \), we can follow these steps:

### Step 1: Approximate \( 34.993 \)
The value \( 34.993 \) is very close to \( 35 \). For simplicity in calculations, we can round it to \( 35 \).

**Hint:** When dealing with numbers that are close to whole numbers, rounding can simplify calculations.

### Step 2: Approximate \( \sqrt{6354} \)
Next, we need to find the approximate value of \( \sqrt{6354} \). We know that:
- \( \sqrt{6400} = 80 \) (since \( 80^2 = 6400 \))
- \( \sqrt{6250} \) is slightly less than \( 80 \).

Since \( 6354 \) is between \( 6250 \) and \( 6400 \), we can estimate \( \sqrt{6354} \) to be approximately \( 80 \).

**Hint:** When estimating square roots, find the nearest perfect squares to help with approximation.

### Step 3: Multiply the approximated values
Now we can multiply the approximated values:
\[ \sqrt{6354} \approx 80 \quad \text{and} \quad 34.993 \approx 35 \]
So, we calculate:
\[ 80 \times 35 \]

### Step 4: Perform the multiplication
Calculating \( 80 \times 35 \):
\[ 80 \times 35 = 2800 \]

### Conclusion
Thus, the approximate value that should come in place of the question mark (?) is \( 2800 \).

**Final Answer:** \( 2800 \)

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