Question

Given that √2 is irrational, prove that 5+3✓2 is an irrational number.​

Answer 1

Answer:

Assume that 5+ 3root 2 as rational.

So 5+3 root 2 = p/q ( where p and q are co prime numbers )

3root 2 = p/q - 5

3root 2 = p-5q / q

root 2 = p-5q/ 3q

root 2 is irrational....

so p - 5q/ 3q is also irrational....

Therefore 5+3 root 2 is irrational