Question

# Give an example for each of the following:(i) The product of two irrational numbers is a rational number.(ii) The product of two irrational numbers is an irrational number.

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Solution

## 1- The product of two irrational numbers is an irrational number. The numbers √2 and √3 are both irrational and so √2.√3 = √2.3 = √6 So the product of √2 and √3 both irrational is √6 (which is also irrational) 2- The product of two irrational numbers is a rational number. The numbers √2 and √8 are irrational , but √2.√8 = √16 = 4 is rational number. So the product of √2 and √8 which are irrational numbers is 4 (rational number)

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