Prove that the following is irrational : 6+√2 [3 MARKS]
Concept : 1 Mark
Application : 1 Mark
Proof : 1 Mark
Lets assume that (6+√2) is rational.
It means that we have co-prime integers a and b (b≠0) such that ab=6+√2
⇒ab−6=√2
⇒(a−6b)b=√2 ...(1)
a and b are integers. It means L.H.S of (1) is rational.
But we know that √2 is irrational.
⇒L.H.S≠R.H.S
This contradiction arises because our assumption is wrong.
∴(6+√2) cannot be rational.
Hence, (6+√2) is irrational.