Question

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

Answer 1

Answer:

let us assume that 2 root 5 - 3 is rational no.

so, 2 root 5 - 3 = p/q , where p and q are some integers and q # 0

=> root 5 = p + 3q / 2q

this shows that root 5 is rational no. because 3 , 2 , p and q are some integers.

but we know that root 5 is irrational no.

=> 2 root 5 - 3 is irrational no.