It is proved that rational number multiplied by irrational number is still irrational number. E.g. It is proved that rational number multiplied by irrational number is still irrational number. Such as a question

It is proved that rational number multiplied by irrational number is still irrational number. E.g. It is proved that rational number multiplied by irrational number is still irrational number. Such as a question

The definition of rational number and irrational number can be used to prove it.
Integers and fractions are generally called rational numbers, that is to say, for a rational number, it must be expressed as a/b a, b is an integer, otherwise, it is an irrational number.
Proof:Assume x is a rational number and y is a irrational number,
Then there exist two integers a,b that x = a/b.
The product of x,y is z = xy=ay/b.(1)
If z is a rational number,then there exist two integer c,d that z = c/d (2)
From (1)(2) we get ay /b=c/ d,that is y =bc/ad.
As we know,a,b,c,d are all integers ,which make y must be a rational number,that is a contravention.
Thus,z must be a irrational number.

Is 2th of pi a rational number or an irrational number If pi is an irrational number, is that 2th of pi an irrational number, Is Part 2 Rational or Irrational If pi is an irrational number, is that 2th of pi an irrational number,

It's an irrational number.