Question

Prove that 1÷√2 is irrational​

Answer 1

Let us assume

1/√2

is rational.

So we can write this number as

1

V2

a

b

(1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) multiply by v2 both sides, we get

1 =

av2

b

Now, divide by b, we get

b = av2 or b a V2

Here, a and b are integers so, b a is a rational

number,

so v 2 should be a rational number.

But 2 is a irrational number, so it is contradictory

so 1/ √2 is irrational.