Question

Prove that √3 - √5 is an irrational number​

Answer 1

Step-by-step explanation:

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

Answer:

$\sqrt{3} - \sqrt{5} \: \: is \: irrational$

Step-by-step explanation:

$\sqrt{3} is \: irrational$

$\sqrt{5} \: \: is \: irrational$

(irarional number)-(irrational number)

=irrational number