Which of the following statements (s) is/are TRUE ?
I. `sqrt(144)xxsqrt(36) lt root3(125)xxsqrt(121)`
II. `sqrt(324)+sqrt(49) lt root3(216)xsqrt(9)`

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/are true, we will evaluate both statements step by step.

### Statement I:
\[ \sqrt{144} \times \sqrt{36} < \sqrt[3]{125} \times \sqrt{121} \]

**Step 1:** Calculate \(\sqrt{144}\) and \(\sqrt{36}\).
- \(\sqrt{144} = 12\)
- \(\sqrt{36} = 6\)

**Step 2:** Multiply the results from Step 1.
\[ 12 \times 6 = 72 \]

**Step 3:** Calculate \(\sqrt[3]{125}\) and \(\sqrt{121}\).
- \(\sqrt[3]{125} = 5\)
- \(\sqrt{121} = 11\)

**Step 4:** Multiply the results from Step 3.
\[ 5 \times 11 = 55 \]

**Step 5:** Compare the two results.
\[ 72 < 55 \quad \text{(This is FALSE)} \]

### Statement II:
\[ \sqrt{324} + \sqrt{49} < \sqrt[3]{216} \times \sqrt{9} \]

**Step 1:** Calculate \(\sqrt{324}\) and \(\sqrt{49}\).
- \(\sqrt{324} = 18\)
- \(\sqrt{49} = 7\)

**Step 2:** Add the results from Step 1.
\[ 18 + 7 = 25 \]

**Step 3:** Calculate \(\sqrt[3]{216}\) and \(\sqrt{9}\).
- \(\sqrt[3]{216} = 6\)
- \(\sqrt{9} = 3\)

**Step 4:** Multiply the results from Step 3.
\[ 6 \times 3 = 18 \]

**Step 5:** Compare the two results.
\[ 25 < 18 \quad \text{(This is FALSE)} \]

### Conclusion:
Both statements are false. Therefore, the correct answer is that neither statement is true.

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

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