`8787div343xxsqrt(50)=?`

Options

A. 250
B. 140
C. 180
D. 100

Explanation

To solve the expression \( 8787 \div 343 \times \sqrt{50} \), we will follow these steps:

### Step 1: Divide 8787 by 343
First, we need to perform the division:

\[ \frac{8787}{343} \approx 25.60618 \]

For approximation, we can round this to:

\[ \approx 25 \]

### Step 2: Simplify \(\sqrt{50}\)
Next, we simplify \(\sqrt{50}\):

\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

### Step 3: Approximate \(\sqrt{2}\)
Now, we can approximate \(\sqrt{2}\):

\[ \sqrt{2} \approx 1.41 \]

Thus, we can express \(\sqrt{50}\) as:

\[ \sqrt{50} \approx 5 \times 1.41 = 7.05 \]

### Step 4: Multiply the results
Now, we multiply the results from Step 1 and Step 3:

\[ 25 \times 7.05 \approx 175.00 \]

### Step 5: Find the closest approximation
Finally, we need to find the closest approximation to 175 from the given options. The options are:

- 250 (too high)
- 140 (too low)
- 180 (closest)

Thus, the closest approximation is:

\[ \approx 180 \]

### Final Answer:
The answer to the expression \( 8787 \div 343 \times \sqrt{50} \) is approximately \( 180 \).

---