Question

show that 1/√2 is irrational if √2 is given irrational​

Answer 1

Answer:

to do that,

say,

let us assume that 1/√2 is an irrational number.

and find two integer such that[ 1/√2=a/b]. -eq -1

simplify eq -1

b/a = √2. [by cross multiplication]

but it contradict the fact that √2 is irrational .

so, this contradiction arisen due to our incorrect assuption that 1/√2 is rational.

It Show that 1/√2 is irrational .

hence proved!