Question

Prove that 5+√3 is irrational​

Answer 1

Answer:

let us assume to the contrary that 5-root3 is rational

=>5-root3=a/b     (where a and b are co primes and b not equal to zero)

=>root3=5b-a/b

Here a and b are integers, so 5-a/b is rational , hence root3 is also rational.

But this contradicts our fact that root 3 is irrational.

This contradiction has arisen bcoz of our incorrect assumption that 5-root3 is rational.

hence 5-root3 is irrational

Answer 2

Step-by-step explanation:

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− √3 is irrational