Question

prove that 1/√2 is irrational

Answer 1

Let us assume that 1/√2 is a rational number and it is equal to another rational number a/b,where b is not equal to zero.

Therefore,1/√2=a/b

1=a/b×√2

√2= b/a

We know that √2 is an irrational number.so,our assumption is wrong

1/√2 is an irrational number.

Hence Proved

Answer 2

Answer:

let 1/√2 is rational and 1/√2=p/q,q is not equal to 0 and p is not equal to 0

q/p=√2

clearly, LHS is rational and RHS is irrational

Rational cannot be equal to irrational

This contradiction has arisen due to our wrong assumption that 1/√2 is rational.

1/√2 is irrational.

hence problem solved