Which of the following statement(s) is/are TRUE?
I. `2sqrt3 gt 3sqrt2`
II. `4sqrt2 gt 2sqrt8`

Options

A. Only I
B. Only II
C. Neither I nor II
D. Both I and II

Answer

To determine which of the statements are true, we will evaluate each statement step by step.

### Statement I: \( 2\sqrt{3} > 3\sqrt{2} \)

1. **Calculate \( 2\sqrt{3} \)**:
- The value of \( \sqrt{3} \) is approximately \( 1.732 \).
- Therefore, \( 2\sqrt{3} = 2 \times 1.732 \approx 3.464 \).

2. **Calculate \( 3\sqrt{2} \)**:
- The value of \( \sqrt{2} \) is approximately \( 1.414 \).
- Therefore, \( 3\sqrt{2} = 3 \times 1.414 \approx 4.242 \).

3. **Compare the two values**:
- We have \( 2\sqrt{3} \approx 3.464 \) and \( 3\sqrt{2} \approx 4.242 \).
- Since \( 3.464 < 4.242 \), the statement \( 2\sqrt{3} > 3\sqrt{2} \) is **FALSE**.

### Statement II: \( 4\sqrt{2} > 2\sqrt{8} \)

1. **Calculate \( 4\sqrt{2} \)**:
- We already know \( \sqrt{2} \approx 1.414 \).
- Therefore, \( 4\sqrt{2} = 4 \times 1.414 \approx 5.656 \).

2. **Calculate \( 2\sqrt{8} \)**:
- First, simplify \( \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \).
- Therefore, \( 2\sqrt{8} = 2 \times 2\sqrt{2} = 4\sqrt{2} \).
- Thus, \( 2\sqrt{8} = 4\sqrt{2} \).

3. **Compare the two values**:
- We have \( 4\sqrt{2} \) on both sides.
- Therefore, \( 4\sqrt{2} = 2\sqrt{8} \), which means the statement \( 4\sqrt{2} > 2\sqrt{8} \) is **FALSE**.

### Conclusion:
Both statements are false. Therefore, the answer is that neither statement I nor statement II is true.

### Final Answer:
Neither statement I nor statement II is true.

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