Question

prove that 5 + √3 is irrational.

Answer 1

Let 5+√3 be rational number.

A rational number can be written in the form of p/q where p,q are integers.

5+√3=p/q
√3=p/q-5
√3=(p-5q)/q

p,q are integers,then (p-5q)/q is a rational number.
Then,√3 is also a rational number.
But this contradicts the fact that √3 is an irrational number.
Therefore,our supposition is false.
So,5+√3 is an irrational number.

Hence proved.

Answer 2

Rule of an irrational no. is that it should be terminating or non terminating and non recurring

root 3 satisfy this condition

any no. added with an irrational will be an ireational so the ans is irrational