Question

prove that 5+√3 is irrational​

Answer 1

Answer:

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

= 5 +√3 = p/q

= √3 = (p - 5q) / 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

Answer 2

let us assume that 5+root 3 is not an irrational number

If 5+root 3 is rational then let 5+root 3=p/q

Therefore,We get root 3=p/q-5

In this equation left side is an irrational number and right side rational number, which contradictory, so 5+root3 is not a rational number but it is an irrational number.