Prove-if-a-rational-times-an-irrational-can-result-in-a-rational-

Question Number 9510 by FilupSmith last updated on 11/Dec/16

Prove if a rational times an irrational

can result in a rational .

Answered by geovane10math last updated on 11/Dec/16

A r a t i o n a l t i m e s a n i r r a t i o n a l a l y a w s

i s a i r r a t i o n a l .

q_{m} = r a t i o n a l

i_{m} = i r r a t i o n a l

S u p p o s e t h a t,

q_{m} \cdot i_{m} = q_{n}

i_{m} = \frac{q_{n}}{q_{m}} (1)

\frac{q_{n}}{q_{m}} i s r a t i o n a l, s o (1) i s f a l s e