Question

prove square root 3 + square root 5 is irrational number

Answer 1

root 3 and root five are irrational because they are not perfect square

Answer 2

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

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