Question

Prove that 5-sqrt(3) is irrational given that sqrt(3) is irrational​

Answer 1

Answer:

or

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

⇒5−

3

=

q

p

⇒

3

=

q

5q−p

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