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.
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