Find the value of $\sqrt{36.1 imes 102.4}$ :

Q: Find the value of $\sqrt{36.1 \times 102.4}$ :

To find the value of $\sqrt{36.1 \times 102.4}$, we need to perform the multiplication first and then take the square root of the result. 1. **Calculate the Product:** \[ 36.1 \times 102.4 = 3699.84 \] 2. **Calculate the Square Root:** \[ \sqrt{3699.84} \approx 60.8 \] Now, let's justify why Option 2 is correct and why the other options are incorrect: ### Justification for Option 2 (60.8): - The calculated square root of the product $3699.84$ is approximately $60.8$. This matches Option 2 exactly, confirming it as the correct answer. ### Explanation for Incorrectness of Other Options: - **Option 1 (58.8):** The value $58.8$ is less than the calculated square root $60.8$. Therefore, it does not match the result of $\sqrt{3699.84}$. - **Option 3 (60.2):** The value $60.2$ is close but still less than the calculated square root $60.8$. It does not accurately represent the square root of $3699.84$. - **Option 4 (62.2):** The value $62.2$ is greater than the calculated square root $60.8$. Hence, it does not match the result of $\sqrt{3699.84}$. In conclusion, Option 2 (60.8) is the correct answer as it precisely matches the calculated square root of the product $36.1 \times 102.4$.

Question

Find the value of $\sqrt{36.1 	imes 102.4}$ :

Accepted Answer

To find the value of $\sqrt{36.1 \times 102.4}$, we need to perform the multiplication first and then take the square root of the result.

1. **Calculate the Product:**
   $$
   36.1 \times 102.4 = 3699.84
   $$

2. **Calculate the Square Root:**
   $$
   \sqrt{3699.84} \approx 60.8
   $$

Now, let's justify why Option 2 is correct and why the other options are incorrect:

### Justification for Option 2 (60.8):
- The calculated square root of the product $3699.84$ is approximately $60.8$. This matches Option 2 exactly, confirming it as the correct answer.

### Explanation for Incorrectness of Other Options:
- **Option 1 (58.8):** The value $58.8$ is less than the calculated square root $60.8$. Therefore, it does not match the result of $\sqrt{3699.84}$.
- **Option 3 (60.2):** The value $60.2$ is close but still less than the calculated square root $60.8$. It does not accurately represent the square root of $3699.84$.
- **Option 4 (62.2):** The value $62.2$ is greater than the calculated square root $60.8$. Hence, it does not match the result of $\sqrt{3699.84}$.

In conclusion, Option 2 (60.8) is the correct answer as it precisely matches the calculated square root of the product $36.1 \times 102.4$.