Question

prove that
$1 \div \sqrt{2}$
is irrational​

Answer 1

1/√2 is an irrational because ( irrational number is whose denominator is divisible by either 2 or 7 )

so 1/√2 is an irrational number

Answer 2

Step-by-step explanation:

To prove 1/√2 is irrational

Let us assume that √2 is irrational

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

q/p=√2

q=√2p

Squaring on both the sides

q²=2p²....(1)

By theorem

q is divisible by 2

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

putting the value of q on equation 1

2p²=q²=2c²=4c²

p²=4c²/2

p²/2=c²

by theorem p is also divisible by 2

But p and q are co-prime

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

Therefore 1/√2 is irrational