Answer:Prove that √5 is an irrational number.

Use Euclid's Division Lemma to show that the square of any positive integer is either of the form 3n or (3n + 1) for some integer n.

Show that the square of any positive odd integer is of the form 8n + 1, for some integer n.

Prove that 2 − 3√5 is an irrational number.

Find two irrational numbers lying between √2 and √3.