Question

Which number produces an irrational number when multiplied by -1.25? (WORTH 12 POINTS!!)

Answer 1

A rational times an irrational is irrational.

Explanation:

Let x be an irrational number and

`p=(m)/(n)` be a rational number

We want to show that
`xp` is irrational through contradiction:

Assume
`xp = q =(a)/(b)` is rational. Rearranging, we get ;

`(xm)/(n) = (a)/(b) \\\\Cross \:multiply\\bmx = an\\\\Divide \:both\:sides\:of\:the\:equation\:by\:bm\\\\x = (an)/(bm)`

which is a contradiction.

Therefore, a rational times an irrational is irrational.