Show that ` 1/sqrt2` is irrational.

Explanation

Let us assume, to the contrary that` 1/sqrt2` is rational.
Then , there exist co-prime a and b ` (b ne 0)` such that
` 1/sqrt2 = a/b Rightarrow sqrt2 = b/a`
Since a and b are integers , so ` a/b` is rational.
Thus, `sqrt2` is also rational.
But, this contradicts the fact that ` sqrt2` is irrational. So, our assumption is incorrect.
Hence, `1/sqrt2` is irrational.