Question

Prove that √3+√5 is an irrational number.

Answer 1

Let root 3 + roof 5 be rational

root 3 + root 5 = P/q

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

3 +5 + 2 root 15 = P sq/q Sq

root 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

Answer 2

First prove √3 or √5 is in ur own method and conclude that any number added to a irrational in irrational