The product of two irrational number is

Options

A. always irrational
B. always rational
C. always an integer
D. sometime rational and sometimes irrational

Answer

To solve the question regarding the product of two irrational numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Two Irrational Numbers**:
Let's take two irrational numbers, for example, \( \sqrt{8} \) and \( \sqrt{2} \).

2. **Calculate the Product**:
We calculate the product of these two numbers:
\[ \sqrt{8} \times \sqrt{2} = \sqrt{8 \times 2} = \sqrt{16} \]

3. **Simplify the Result**:
Now, simplify \( \sqrt{16} \):
\[ \sqrt{16} = 4 \]
Here, \( 4 \) is a rational number.

4. **Check Another Pair of Irrational Numbers**:
Now, let's take another pair of irrational numbers, \( \sqrt{5} \) and \( \sqrt{2} \).

5. **Calculate the Product**:
We calculate the product of these two numbers:
\[ \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} \]

6. **Determine the Nature of the Result**:
The number \( \sqrt{10} \) is also an irrational number.

7. **Conclusion**:
From these examples, we can conclude that the product of two irrational numbers can be either a rational number or an irrational number. Thus, the answer to the question is that the product of two irrational numbers can be sometimes rational and sometimes irrational.

### Final Answer:
The product of two irrational numbers can be both rational and irrational.

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