Find the value of `sqrt(36.1xx102.4)`

Options

A. 58 .8
B. 60 .8
C. 60.2
D. 62 .2

Answer

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

### Step-by-Step Solution:

1. **Rewrite the Expression**:
We start with the expression under the square root:
\[ \sqrt{36.1 \times 102.4} \]
We can express \( 36.1 \) and \( 102.4 \) in a more manageable form. Notice that \( 36.1 \) can be rewritten as \( \frac{361}{10} \) and \( 102.4 \) can be rewritten as \( \frac{1024}{10} \). Thus, we have:
\[ \sqrt{36.1 \times 102.4} = \sqrt{\left(\frac{361}{10}\right) \times \left(\frac{1024}{10}\right)} \]

2. **Combine the Fractions**:
Now, we can combine the fractions:
\[ = \sqrt{\frac{361 \times 1024}{100}} \]

3. **Separate the Square Root**:
We can separate the square root of the fraction:
\[ = \frac{\sqrt{361 \times 1024}}{\sqrt{100}} \]

4. **Calculate the Square Root of 100**:
The square root of \( 100 \) is \( 10 \):
\[ = \frac{\sqrt{361 \times 1024}}{10} \]

5. **Calculate the Square Roots**:
Now, we need to find \( \sqrt{361} \) and \( \sqrt{1024} \):
- \( \sqrt{361} = 19 \)
- \( \sqrt{1024} = 32 \)

6. **Multiply the Square Roots**:
Now we multiply these results:
\[ \sqrt{361 \times 1024} = 19 \times 32 \]

7. **Calculate \( 19 \times 32 \)**:
We can calculate \( 19 \times 32 \):
\[ 19 \times 32 = 608 \]

8. **Final Calculation**:
Now, we substitute back into our expression:
\[ = \frac{608}{10} = 60.8 \]

### Final Answer:
Thus, the value of \( \sqrt{36.1 \times 102.4} \) is \( 60.8 \).