`sqrt(3.38)xxsqrt(3.92)=`___

Options

A. 1.82
B. 1.72
C. 3.64
D. 3.44

Answer

To solve the expression \(\sqrt{3.38} \times \sqrt{3.92}\), we can follow these steps:

### Step 1: Rewrite the square roots
We can express the numbers under the square roots in a way that removes the decimal points.
\[ \sqrt{3.38} = \sqrt{\frac{338}{100}} \quad \text{and} \quad \sqrt{3.92} = \sqrt{\frac{392}{100}} \]

### Step 2: Combine the square roots
Using the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\), we can combine the two square roots:
\[ \sqrt{3.38} \times \sqrt{3.92} = \sqrt{\frac{338}{100} \times \frac{392}{100}} = \sqrt{\frac{338 \times 392}{10000}} \]

### Step 3: Calculate \(338 \times 392\)
Now, we need to calculate \(338 \times 392\).
- First, we can break it down:
\[ 338 \times 392 = 338 \times (400 - 8) = 338 \times 400 - 338 \times 8 \]
Calculating each part:
\[ 338 \times 400 = 135200 \quad \text{and} \quad 338 \times 8 = 2704 \]
Thus,
\[ 338 \times 392 = 135200 - 2704 = 132496 \]

### Step 4: Substitute back into the square root
Now we substitute back into our expression:
\[ \sqrt{\frac{132496}{10000}} = \frac{\sqrt{132496}}{\sqrt{10000}} = \frac{\sqrt{132496}}{100} \]

### Step 5: Calculate \(\sqrt{132496}\)
Next, we need to find \(\sqrt{132496}\).
- We can factor \(132496\) to find its square root.
- It turns out that \(132496 = 364^2\), so:
\[ \sqrt{132496} = 364 \]

### Step 6: Final calculation
Now, we can finalize our expression:
\[ \frac{364}{100} = 3.64 \]

Thus, the final answer is:
\[ \sqrt{3.38} \times \sqrt{3.92} = 3.64 \]

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