Question & Answer » Mathematics Questions » Is the Product of a Rational and Irrational Number Always Irrational Give an Example

Is the Product of a Rational and Irrational Number Always Irrational Give an Example

Answer: An irrational number is the product of a rational and an irrational number.

If A is a rational number and B is an irrational number, then AB is also an irrational number 

Example 1:

Considering 

  • A = 3  
  • B = √5

AB = 3×√5

3×√5 is an irrational number.

Example 2:

If 4 is a rational number and √3 is an irrational number.

Then their product is 4√3.

As a result, if the rational number is greater than zero, the product of a rational and irrational amount has always been an irrational number.