Which of the following is/are TRUE ?
I. `(2sqrt(26)) gt (3sqrt(35))`
II. `(3sqrt(37) gt (4sqrt(50))`

Options

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

Answer

To determine which of the statements is true, we will evaluate each inequality step by step.

### Step 1: Evaluate Statement I: \(2\sqrt{26} > 3\sqrt{35}\)

1. **Calculate \(2\sqrt{26}\)**:
- First, find the value of \(\sqrt{26}\).
- \(\sqrt{26} \approx 5.099\) (using a calculator or estimation).
- Now, multiply by 2:
\[ 2\sqrt{26} \approx 2 \times 5.099 \approx 10.198 \]

2. **Calculate \(3\sqrt{35}\)**:
- First, find the value of \(\sqrt{35}\).
- \(\sqrt{35} \approx 5.916\).
- Now, multiply by 3:
\[ 3\sqrt{35} \approx 3 \times 5.916 \approx 17.748 \]

3. **Compare the two results**:
- Now we compare \(10.198\) and \(17.748\).
- Since \(10.198 < 17.748\), we conclude that:
\[ 2\sqrt{26} < 3\sqrt{35} \]
- Therefore, Statement I is **FALSE**.

### Step 2: Evaluate Statement II: \(3\sqrt{37} > 4\sqrt{50}\)

1. **Calculate \(3\sqrt{37}\)**:
- First, find the value of \(\sqrt{37}\).
- \(\sqrt{37} \approx 6.083\).
- Now, multiply by 3:
\[ 3\sqrt{37} \approx 3 \times 6.083 \approx 18.249 \]

2. **Calculate \(4\sqrt{50}\)**:
- First, find the value of \(\sqrt{50}\).
- \(\sqrt{50} \approx 7.071\).
- Now, multiply by 4:
\[ 4\sqrt{50} \approx 4 \times 7.071 \approx 28.284 \]

3. **Compare the two results**:
- Now we compare \(18.249\) and \(28.284\).
- Since \(18.249 < 28.284\), we conclude that:
\[ 3\sqrt{37} < 4\sqrt{50} \]
- Therefore, Statement II is also **FALSE**.

### Final Conclusion:
Both statements I and II are FALSE.