The product of a rational and irrational number is always irrational. We will see this with an example.

We know that every rational number is a whole number. The product of a rational and an irrational number is an irrational number.

If x is a rational number and y is an irrational number

Then xy is irrational.

Example: a = 2 and b = √3

ab = 2 √3

2 √3 is an irrational number.

Consider the rational number 0 and irrational number √3

Multiplication of rational and irrational number is 0.

= 0 x √3

= 0

So, when the rational number is 0 then the product of a rational and irrational number is always a rational number.

Let’s see 4 x √3

=4√3

Thus, if a rational number is non-zero, the product of a rational and irrational number is always an irrational number.

## FAQ

### What is the product of a rational and an irrational number?

the product of a rational and an irrational number is always Irrational.

### On what condition the product of a rational and an irrational number is Rational?

When the Rational number is zero the product is Rational.