$ ext{The value of } \sqrt{\frac{.081 imes .484}{.0064 imes 6.25}} ext{ is :}$

Q: $\text{The value of } \sqrt{\frac{.081 \times .484}{.0064 \times 6.25}} \text{ is :}$

To determine the value of $\sqrt{\frac{.081 \times .484}{.0064 \times 6.25}}$, we need to simplify the expression step by step. 1. **Calculate the numerator:** \[ .081 \times .484 = 0.039204 \] 2. **Calculate the denominator:** \[ .0064 \times 6.25 = 0.04 \] 3. **Form the fraction:** \[ \frac{0.039204}{0.04} \] 4. **Simplify the fraction:** \[ \frac{0.039204}{0.04} = 0.9801 \] 5. **Calculate the square root:** \[ \sqrt{0.9801} = 0.99 \] Thus, the value of $\sqrt{\frac{.081 \times .484}{.0064 \times 6.25}}$ is 0.99, which corresponds to Option 4. ### Explanation for Other Options: - **Option 1 (9):** The value 9 is significantly larger than the calculated result of 0.99. The square root of a number less than 1 will also be less than 1, making 9 an incorrect choice. - **Option 2 (0.9):** While 0.9 is closer to the correct answer than 9, it is still not accurate. The precise calculation yields 0.99, not 0.9. - **Option 3 (99):** Similar to Option 1, 99 is much larger than the calculated result. The square root of a number less than 1 cannot be greater than 1, making 99 an incorrect choice. Therefore, based on the calculations and logical reasoning, Option 4 (0.99) is indeed the correct answer.

Question

$	ext{The value of } \sqrt{\frac{.081 	imes .484}{.0064 	imes 6.25}} 	ext{ is :}$

Accepted Answer

To determine the value of $\sqrt{\frac{.081 \times .484}{.0064 \times 6.25}}$, we need to simplify the expression step by step.

1. **Calculate the numerator:**
   $$
   .081 \times .484 = 0.039204
   $$

2. **Calculate the denominator:**
   $$
   .0064 \times 6.25 = 0.04
   $$

3. **Form the fraction:**
   $$
   \frac{0.039204}{0.04}
   $$

4. **Simplify the fraction:**
   $$
   \frac{0.039204}{0.04} = 0.9801
   $$

5. **Calculate the square root:**
   $$
   \sqrt{0.9801} = 0.99
   $$

Thus, the value of $\sqrt{\frac{.081 \times .484}{.0064 \times 6.25}}$ is 0.99, which corresponds to Option 4.

### Explanation for Other Options:

- **Option 1 (9):** 
  The value 9 is significantly larger than the calculated result of 0.99. The square root of a number less than 1 will also be less than 1, making 9 an incorrect choice.

- **Option 2 (0.9):**
  While 0.9 is closer to the correct answer than 9, it is still not accurate. The precise calculation yields 0.99, not 0.9.

- **Option 3 (99):**
  Similar to Option 1, 99 is much larger than the calculated result. The square root of a number less than 1 cannot be greater than 1, making 99 an incorrect choice.

Therefore, based on the calculations and logical reasoning, Option 4 (0.99) is indeed the correct answer.