Question

The rationalising factor of `sqrt(2) + 1` is ______.

Options

• 1

• `sqrt(2)`

• `1/(sqrt(2) - 1)`

• `sqrt(2) - 1`

Answer 1

The rationalising factor of `sqrt(2) + 1` is `underlinebb(sqrt(2) - 1)`.

Explanation:

The rationalising factor of `sqrt(2) + 1` is the conjugate term `sqrt(2) - 1`. 

Multiplying `sqrt(2) + 1` by `sqrt(2) - 1` results in a rational number:

`(sqrt(2) + 1)(sqrt(2) - 1)`

= `(sqrt(2))^2 - (1)^2`

= 2 – 1

= 1

So, `sqrt(2) - 1` rationalises the expression.

Thus, the rationalising factor of `sqrt(2) + 1` is `sqrt(2) - 1`.