Which of the following is /are true?

Options

A. `sqrt(6)xxsqrt(6)` is an irrational number.
B. `sqrt(5)xxsqrt(25)` is a rational number.
C. Both a and b
D. Neither a nor b

Answer

To determine which of the statements are true, let's analyze each option step-by-step.

### Step 1: Analyze Option 1
**Statement:** Root 6 multiplied by Root 6 is an irrational number.

**Calculation:**
- We can express this mathematically as:
\[ \sqrt{6} \times \sqrt{6} = \sqrt{6 \times 6} = \sqrt{36} = 6 \]
- Since 6 is a whole number, it is a rational number.

**Conclusion for Option 1:**
- Therefore, the statement is **false**.

### Step 2: Analyze Option 2
**Statement:** Root 5 multiplied by Root 25 is an irrational number.

**Calculation:**
- We can express this mathematically as:
\[ \sqrt{5} \times \sqrt{25} = \sqrt{5 \times 25} = \sqrt{125} \]
- We can simplify \(\sqrt{125}\):
\[ \sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5} \]
- Since \(5\sqrt{5}\) is not a whole number and \(\sqrt{5}\) is irrational, \(5\sqrt{5}\) is also irrational.

**Conclusion for Option 2:**
- Therefore, the statement is **true**.

### Step 3: Analyze Option 3
**Statement:** Both A and B are true.

**Conclusion for Option 3:**
- Since Option 1 is false and Option 2 is true, this statement is **false**.

### Step 4: Analyze Option 4
**Statement:** Neither A nor B are true.

**Conclusion for Option 4:**
- Since Option 1 is false and Option 2 is true, this statement is also **false**.

### Final Conclusion:
- The only true statement is that Option 2 is true. Therefore, the correct answer is that **Option 2 is true**, while Options 1 and 3 are false.

---