If x is an irrational number and

Scolfaro2y

Scolfaro2y

Answered question

2022-05-21

If x is an irrational number and r is a rational number then x r is an irrational number.

Answer & Explanation

Harley Fitzpatrick

Harley Fitzpatrick

Beginner2022-05-22Added 13 answers

if you take x = 2 and r = 0,
x r = 2 0 = 0 ,
which is rational, not irrational.

However, suppose that r 0. Then suppose towards contradiction that x is irrational and r is rational, but r x is not irrational, i.e. r x is rational. Then write r x = s, where s is rational. Since r 0, this implies x = s r

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