What is the square root of $\frac{0.324 imes 0.64 imes 129.6}{0.729 imes 1.024 imes 36}$

Q: What is the square root of $\frac{0.324 \times 0.64 \times 129.6}{0.729 \times 1.024 \times 36}$

To determine the square root of the given expression $\frac{0.324 \times 0.64 \times 129.6}{0.729 \times 1.024 \times 36}$, we need to simplify the expression step by step and verify why Option 4, which is 1, is indeed the correct answer. ### Step-by-Step Explanation: 1. **Simplify the Numerator:** - Calculate $0.324 \times 0.64 \times 129.6$. - $0.324 \times 0.64 = 0.20736$. - $0.20736 \times 129.6 = 26.870016$. 2. **Simplify the Denominator:** - Calculate $0.729 \times 1.024 \times 36$. - $0.729 \times 1.024 = 0.746496$. - $0.746496 \times 36 = 26.870016$. 3. **Form the Fraction:** - The fraction becomes $\frac{26.870016}{26.870016} = 1$. 4. **Calculate the Square Root:** - The square root of 1 is 1. ### Justification for Option 4: - The calculation shows that the expression simplifies to 1, and the square root of 1 is indeed 1. Therefore, Option 4 is correct. ### Explanation for Incorrectness of Other Options: - **Option 1 (4):** The square root of 1 is not 4. - **Option 2 (3):** The square root of 1 is not 3. - **Option 3 (2):** The square root of 1 is not 2. Thus, based on the calculations and logical reasoning, Option 4 is the correct answer, as the square root of the simplified expression is indeed 1.

Question

What is the square root of $\frac{0.324 	imes 0.64 	imes 129.6}{0.729 	imes 1.024 	imes 36}$

Accepted Answer

To determine the square root of the given expression $\frac{0.324 \times 0.64 \times 129.6}{0.729 \times 1.024 \times 36}$, we need to simplify the expression step by step and verify why Option 4, which is 1, is indeed the correct answer.

### Step-by-Step Explanation:

1. **Simplify the Numerator:**
   - Calculate $0.324 \times 0.64 \times 129.6$.
   - $0.324 \times 0.64 = 0.20736$.
   - $0.20736 \times 129.6 = 26.870016$.

2. **Simplify the Denominator:**
   - Calculate $0.729 \times 1.024 \times 36$.
   - $0.729 \times 1.024 = 0.746496$.
   - $0.746496 \times 36 = 26.870016$.

3. **Form the Fraction:**
   - The fraction becomes $\frac{26.870016}{26.870016} = 1$.

4. **Calculate the Square Root:**
   - The square root of 1 is 1.

### Justification for Option 4:

- The calculation shows that the expression simplifies to 1, and the square root of 1 is indeed 1. Therefore, Option 4 is correct.

### Explanation for Incorrectness of Other Options:

- **Option 1 (4):** The square root of 1 is not 4.
- **Option 2 (3):** The square root of 1 is not 3.
- **Option 3 (2):** The square root of 1 is not 2.

Thus, based on the calculations and logical reasoning, Option 4 is the correct answer, as the square root of the simplified expression is indeed 1.