Find the value of `sqrt(36.1 xx 102.4)`

Options

A. A)58.8
B. B)60.8
C. C)60.2
D. D)62.2

Answer

To find the value of \( \sqrt{36.1 \times 102.4} \), we can follow these steps:

### Step 1: Rewrite the numbers without decimals
We can express \( 36.1 \) and \( 102.4 \) in a way that makes calculations easier.

\[ 36.1 = \frac{361}{10} \quad \text{and} \quad 102.4 = \frac{1024}{10} \]

### Step 2: Multiply the two fractions
Now, we can multiply these two fractions:

\[ 36.1 \times 102.4 = \left(\frac{361}{10}\right) \times \left(\frac{1024}{10}\right) = \frac{361 \times 1024}{100} \]

### Step 3: Calculate \( 361 \times 1024 \)
Next, we need to calculate \( 361 \times 1024 \).

\[ 361 \times 1024 = 369344 \]

### Step 4: Substitute back into the square root
Now we substitute back into the square root:

\[ \sqrt{36.1 \times 102.4} = \sqrt{\frac{369344}{100}} = \frac{\sqrt{369344}}{\sqrt{100}} \]

### Step 5: Simplify the square root
We know that \( \sqrt{100} = 10 \). Now we need to find \( \sqrt{369344} \).

Calculating \( \sqrt{369344} \):

\[ \sqrt{369344} = 608 \]

### Step 6: Final calculation
Now we can substitute back:

\[ \frac{\sqrt{369344}}{\sqrt{100}} = \frac{608}{10} = 60.8 \]

### Conclusion
Thus, the value of \( \sqrt{36.1 \times 102.4} \) is:

\[ \boxed{60.8} \]