Question

Prove that following numbers are irrationals:
(i) $\frac{2}{\sqrt{7}}$
(ii) $\frac{3}{2\sqrt{5}}$
(iii) $4+\sqrt{2}$
(iv) $5\sqrt{2}$

Answer 1

(i) Let us assume that is rational .Then , there exist positive co primes a and b such that

(ii) Let us assume that $\frac{3}{2\sqrt{5}}$ is rational .Then , there exist positive co primes a and b such that

(iii) Let us assume that is rational .Then , there exist positive co primes a and b such that

(iv) Let us assume that is rational .Then , there exist positive co primes a and b such that