What approximate value will come in place of the question mark (?) in the following questions ?
`sqrt(6889)xxsqrt(4444)-:sqrt(260)=?`

Options

A. 295
B. 450
C. 345
D. 480

Answer

To solve the problem step by step, we need to evaluate the expression given:

\[ \sqrt{6889} \times \sqrt{4444} \div \sqrt{260} = ? \]

### Step 1: Calculate \(\sqrt{6889}\)

First, we find the square root of 6889.

\[ \sqrt{6889} = 83 \]

### Step 2: Calculate \(\sqrt{4444}\)

Next, we approximate \(\sqrt{4444}\). Since \(4444\) is not a perfect square, we can estimate it.

The closest perfect squares are \(66^2 = 4356\) and \(67^2 = 4489\). Thus,

\[ \sqrt{4444} \approx 66.7 \text{ (approximately 67)} \]

### Step 3: Calculate \(\sqrt{260}\)

Now, we find \(\sqrt{260}\).

Again, \(260\) is not a perfect square, but we can estimate:

The closest perfect squares are \(16^2 = 256\) and \(17^2 = 289\). Thus,

\[ \sqrt{260} \approx 16.1 \text{ (approximately 16)} \]

### Step 4: Substitute the values into the expression

Now we substitute the approximate values back into the expression:

\[ \frac{\sqrt{6889} \times \sqrt{4444}}{\sqrt{260}} \approx \frac{83 \times 67}{16} \]

### Step 5: Calculate the numerator

Calculating the numerator:

\[ 83 \times 67 = 5561 \]

### Step 6: Divide by \(\sqrt{260}\)

Now we divide by \(16\):

\[ \frac{5561}{16} \approx 347.5625 \]

### Step 7: Approximate the final value

The approximate value is around \(348\).

### Step 8: Choose the closest option

Looking at the options provided, the closest value to \(348\) is:

**Option C: 345**

Thus, the final answer is:

\[ ? \approx 345 \]

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