Question

prove that 3-✓5 is irrational​

Answer 1

let root 3 + roof 5 be rational

root 3 + root 5 = P/q(root 3 + root 5)

sq=(P/q)sq3 +5 + 2 root 15 = P sq/q

Sqroot I5 = (Psq / qsq -7) 1/2

RHS is rational as all are integers⇒ LHS is also rational but root 15 is irrational⇒ root3 + root 5 is irrational.