product of rational number and irrational number is
irrational
an irrational number.
To understand this, let’s first define what rational and irrational numbers mean.
Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. For example, 2/3, -5/4, 7/1 are all rational numbers.
On the other hand, irrational numbers cannot be expressed as a fraction of two integers. They are decimal numbers that neither terminate nor repeat. For example, pi (π), √2, and e are all irrational numbers.
When we multiply a rational number by an irrational number, the product will be irrational. Let’s take an example:
√2 is an irrational number, and 5/3 is a rational number.
The product of 5/3 and √2 is:
(5/3) x √2 = (5√2) / 3
This number is clearly not rational, since it can’t be expressed as a fraction of two integers. Therefore, the product of a rational number and an irrational number is always an irrational number.
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