Question

PROVE THAT 5-√3 IS IRRARTIONAL?

Answer 1

Question :

Prove that 5 - root 3 is irrational

Answer :

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

⇒5−root 3=qp

⇒root 3 = q5q−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−root 3  is irrational

__________Be Delighted____________

Answer 2

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.

This is contradiction.

Hence our assumption that given number is rational is false

⇒5−√3is irrational

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