Which of the following relation (s) is/are true ?
I. `sqrt2 gt root3(3)`
II.`root3(3) gt sqrt 2`
III. `sqrt2=root3(3)`

Options

A. Only I
B. Only II
C. Neither I nor II
D. Either I or II

Answer

To determine which of the given relations is true, we will evaluate each relation step by step.

### Step 1: Calculate the values of \(\sqrt{2}\) and \(\sqrt[3]{3}\)

1. **Calculate \(\sqrt{2}\)**:
\[ \sqrt{2} \approx 1.414 \]

2. **Calculate \(\sqrt[3]{3}\)**:
\[ \sqrt[3]{3} \approx 1.442 \]

### Step 2: Compare the values

Now we compare the two values we calculated.

- \(\sqrt{2} \approx 1.414\)
- \(\sqrt[3]{3} \approx 1.442\)

### Step 3: Evaluate each relation

1. **Relation I: \(\sqrt{2} > \sqrt[3]{3}\)**
- Since \(1.414 < 1.442\), this relation is **false**.

2. **Relation II: \(\sqrt[3]{3} > \sqrt{2}\)**
- Since \(1.442 > 1.414\), this relation is **true**.

3. **Relation III: \(\sqrt{2} = \sqrt[3]{3}\)**
- Since \(1.414 \neq 1.442\), this relation is **false**.

### Conclusion

From the evaluations above, we find that only Relation II is true.

### Final Answer

The only true relation is:
- **II. \(\sqrt[3]{3} > \sqrt{2}\)**

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