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.