Question

Prove that ½ - √5/3 is irrational. Pls with steps!!!

Answer 1

Let us assume the given number be rational and we will write the given number in p/q form

so,

5-✓3 = p/q

⇒ 3 = 5q−p/q

We observe that LHS is irrational and RHS is rational, which is not possible.

This is contradiction.

Hence our assumption that given number is rational is false

⇒5− ✓3 is irrational

and then subtraction of any irrational number is a irrational number.

Thus proved your question...☺️