Write any two irrational numbers whose product is rational number.

Answer

To find two irrational numbers whose product is a rational number, we can follow these steps:

### Step 1: Choose the first irrational number
Let’s take the first irrational number as \( \sqrt{2} \).

### Step 2: Choose the second irrational number
Now, let’s take the second irrational number as \( \sqrt{2} \) again.

### Step 3: Multiply the two irrational numbers
Now we multiply these two irrational numbers:
\[ \sqrt{2} \times \sqrt{2} = \sqrt{2 \times 2} = \sqrt{4} \]

### Step 4: Simplify the result
Now simplify \( \sqrt{4} \):
\[ \sqrt{4} = 2 \]
Since 2 is a rational number, we have found our first pair of irrational numbers.

### Step 5: Choose another pair of irrational numbers
Next, let’s choose the first irrational number as \( 5\sqrt{7} \) and the second irrational number as \( \sqrt{7} \).

### Step 6: Multiply the second pair of irrational numbers
Now multiply these two irrational numbers:
\[ 5\sqrt{7} \times \sqrt{7} = 5 \times \sqrt{7 \times 7} = 5 \times \sqrt{49} \]

### Step 7: Simplify the result
Now simplify \( \sqrt{49} \):
\[ \sqrt{49} = 7 \]
So, we have:
\[ 5 \times 7 = 35 \]
Since 35 is also a rational number, we have found our second pair of irrational numbers.

### Final Answer
Thus, the two pairs of irrational numbers whose product is a rational number are:
1. \( \sqrt{2} \) and \( \sqrt{2} \) (Product = 2)
2. \( 5\sqrt{7} \) and \( \sqrt{7} \) (Product = 35)

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