Prove by contradiction that if r is irrational, then r^(1/2) is irrational
dnt confuse yourself. both the statements are equivalent. one implies the other and vice-versa.
if sqrt r is rational then r is rational (we proved it)
but r is irrational (as per the question)
that mean sqrt r can't be rational because otherwise r will be rational (a contradiction)
hence sqrt r must be irrational !!