Question

Show that √5-√3 is an
irrational number.​

Answer 1

Answer:

Here we go:-

Step-by-step explanation:

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

Let us assume the given number be rational and we will write the given number in p/q form⇒5− √3 = p/q

⇒ √3 = 5q-p/q

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

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

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

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

3

3 is irrational