Which of the following statement(s) is/are TRUE?
I. `(sqrt(225)+sqrt(441))/(sqrt(256)) gt 2.5`
II. `(sqrt(289)+sqrt(529))/(sqrt(169))gt3`

Options

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

Answer

To solve the problem, we need to evaluate the two statements given and determine which one, if any, is true.

### Statement I:
\[ \frac{\sqrt{225} + \sqrt{441}}{\sqrt{256}} > 2.5 \]

**Step 1**: Calculate \(\sqrt{225}\), \(\sqrt{441}\), and \(\sqrt{256}\).
- \(\sqrt{225} = 15\)
- \(\sqrt{441} = 21\)
- \(\sqrt{256} = 16\)

**Step 2**: Substitute these values into the inequality.
\[ \frac{15 + 21}{16} > 2.5 \]

**Step 3**: Simplify the left side.
\[ \frac{36}{16} > 2.5 \]

**Step 4**: Simplify \(\frac{36}{16}\).
\[ \frac{36}{16} = 2.25 \]

**Step 5**: Check the inequality.
\[ 2.25 > 2.5 \quad \text{(This is FALSE)} \]

### Conclusion for Statement I:
Statement I is FALSE.

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### Statement II:
\[ \frac{\sqrt{289} + \sqrt{529}}{\sqrt{169}} > 3 \]

**Step 1**: Calculate \(\sqrt{289}\), \(\sqrt{529}\), and \(\sqrt{169}\).
- \(\sqrt{289} = 17\)
- \(\sqrt{529} = 23\)
- \(\sqrt{169} = 13\)

**Step 2**: Substitute these values into the inequality.
\[ \frac{17 + 23}{13} > 3 \]

**Step 3**: Simplify the left side.
\[ \frac{40}{13} > 3 \]

**Step 4**: Check the inequality.
- Calculate \(3 \times 13 = 39\).
- Since \(40 > 39\), we have:
\[ \frac{40}{13} > 3 \quad \text{(This is TRUE)} \]

### Conclusion for Statement II:
Statement II is TRUE.

### Final Conclusion:
Only Statement II is true. Therefore, the answer is that only the second statement is true.

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