Question

Prove that V6 is irrational.​

Answer 1

ANSWER

Let us assume that 6 is rational number.

Then it can be represented as fraction of two integers.

Let the lowest terms representation be: 6 = a/b where b is not equal to zero .

* Note that this representation is in lowest terms and hence, a and b have no common factor.

a² = 6b²

From above a² is even. If a² is even, then 'a' should also be even.

⟹a=2c

→ 4c² = 6b²

→ 2c² = 3b²

From above 3b² is even. If 3b² is even, then b² should also be even and again 'b' is even.

But a and b were in lowest form and both cannot be even.

Hence, assumption was wrong .

Thus , V6 is an irrational number.

HOPE IT HELPS ❗.