Question

PROVE THAT 1/ROOT2 IS IRRATIONAL

Answer 1

Step-by-step explanation:

pls refer the above proof....

hope this helps you....

Answer 2

Step-by-step explanation:

We have to prove that 1/√2 is irrational.

We will prove this by contradiction.

Let us assume that √2 is rational.

Therefore, we will get,

=> 1/√2 = p/q (where p and q are co prime)

=> q/p = √2

=> q = √2p

Now, squarring both sides

=>q^2   = 2p^2 .....................(1)

Therefore, this says that,

q is divisible by 2

=> q = 2c ( where c is an integer)

Now, putting the value of q in eqn (1),

=> 2p^2 = q^2

=> 2p^2 = (2c)^2

=> 2p^2 =4c^2

=> p² =4c² /2

=> p^2 = 2c²

=> c^2 = p^2/2

Therefore, we have ,

p is also divisible by 2

But, p and q are coprime.

It means, both can't have commom divisor.

Clearly, it's a contradiction which has arisen due to our wrong assumption.

Hence, 1/√2 is irrational.

Thus, Proved.