Question

prove that 1/√2 is irrational​

Answer 1

Step-by-step explanation:

Let us assume that v2 is irrational

1/12 = p/q (where p and q are co prime)

q/p = v2 q =v2p

squaring both sides

q? = 2p? =

(1)

By theorem q is divisible by 2

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

putting the value of q in equitation 1

2p? = q? = 2c? =4c? %D p? =4c? /2 = 2c? p?/2 = c?

by theorem p is also divisible by 2

But p and q are coprime d:

This is a contradiction which has arisen due to our wrong assumption

.1/V2 is irrational