Is The Product Of a Rational And Irrational Number always Irrational

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.