Question

`1/sqrt(2)` is ______.

Options

• a fraction

• a rational number

• an irrational number

• none of these

Answer 1

`1/sqrt(2)` is an irrational number.

Explanation:

`1/sqrt(2) = 1/sqrt(2) xx sqrt(2)/sqrt(2)`

= `1/2 xx sqrt(2)`

Here, `1/2` is rational and `sqrt(2)` is irrational.

And the product of a rational and an irrational is irrational.

∴ `1/2 xx sqrt(2)` and hence `1/sqrt(2)` is irrational.