Question

Prove that 5 + √3 is irrational.​

Answer 1

Answer:

TO PROVE : 5 + √3 is irrational.

PROOF :

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.

Therefore, 5 + √3 is irrational.