Question

show that √3/2+5 is irrational

Answer 1

Solution.

Let's assume that √3/2+5 is a rational number.

So, √3/2+5 = p/q , q≠0
=> √3/2 = p/q - 5
=> √3/2 = p-5q/q
=> √3 = 2(p-5q)/q
=> √3 = 2p - 10q / q
= integer/integer = a rational number.

Which contradicts the fact that √3 is an irrational number, so the above number is irrational.