Question

the product of any two irrational number is ​

Answer 1

The product of two irrational numbers can be rational or irrational depending upon the numbers.

• The multiplication of surds like $\sqrt{2}$ with itself gives rational numbers
• The multiplication of numbers like $\pi$ or $e$ with their reciprocals gives 1 which is rational.
• The multiplication of unlike surds can give a product that is irrational.
• Multiplication of random combination of irrationals may give irrational.

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Answer 2

Answer:

The product of two irrational numbers is either a rational or an irrational number.

Explanation:

1. It depends on the values of the given numbers whether its product will be rational or irrational.
2. It is not necessary to have an irrational number as the product always.
3. Let us take an example of the multiplication of two irrational numbers, that is, $\sqrt{2} \times \sqrt{2}$.
4. The product of these two irrational numbers is 2, which is a rational number.

Hence, the product of any two irrational numbers can be rational on irrational depending upon the values of the given numbers.

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