`sqrt(5687)xxsqrt(1245)divsqrt(689)=?div13`

Options

A. 840
B. 910
C. 1320
D. 1120

Explanation

To solve the equation \( \sqrt{5687} \times \sqrt{1245} \div \sqrt{689} = ? \div 13 \), we will follow these steps:

### Step 1: Simplify the left-hand side of the equation
We can combine the square roots in the left-hand side:
\[ \sqrt{5687} \times \sqrt{1245} \div \sqrt{689} = \frac{\sqrt{5687 \times 1245}}{\sqrt{689}} \]

### Step 2: Calculate \( \sqrt{5687} \)
To approximate \( \sqrt{5687} \):
- The nearest perfect square to 5687 is 5625, which is \( 75^2 \).
- Therefore, \( \sqrt{5687} \approx 75 \).

### Step 3: Calculate \( \sqrt{1245} \)
To approximate \( \sqrt{1245} \):
- The nearest perfect square to 1245 is 1225, which is \( 35^2 \).
- Therefore, \( \sqrt{1245} \approx 35 \).

### Step 4: Calculate \( \sqrt{689} \)
To approximate \( \sqrt{689} \):
- The nearest perfect square to 689 is 676, which is \( 26^2 \).
- Therefore, \( \sqrt{689} \approx 26 \).

### Step 5: Substitute the approximations into the equation
Now we substitute the approximated values into the equation:
\[ \frac{\sqrt{5687 \times 1245}}{\sqrt{689}} \approx \frac{75 \times 35}{26} \]

### Step 6: Calculate the product
Now we calculate the product:
\[ 75 \times 35 = 2625 \]

### Step 7: Divide by \( \sqrt{689} \)
Now we divide by \( 26 \):
\[ \frac{2625}{26} \approx 101.25 \]

### Step 8: Set up the equation with the right-hand side
Now we set up the equation:
\[ 101.25 = \frac{x}{13} \]

### Step 9: Solve for \( x \)
To find \( x \), we multiply both sides by \( 13 \):
\[ x = 101.25 \times 13 \approx 1316.25 \]

### Step 10: Round to the nearest whole number
Since we are looking for an approximate answer, we round \( 1316.25 \) to \( 1320 \).

### Final Answer
Thus, the final answer is approximately \( 1320 \).

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