Question

Simplify:

`(1 + sqrt(3))(sqrt(2) - 1)`

Answer 1

Given: `(1 + sqrt(3))(sqrt(2) - 1)`

Step wise calculation:

1. Expand using distributive property (FOIL method):

`(1)(sqrt(2)) + (1)(-1) + (sqrt(3))(sqrt(2)) + (sqrt(3))(-1)`

2. Simplify each term:

`sqrt(2) - 1 + sqrt(3) xx sqrt(2) - sqrt(3)`

3. Express the middle product as a single square root:

`sqrt(2) - 1 + sqrt(6) - sqrt(3)`

4. Group terms:

`(sqrt(2) + sqrt(6)) - (1 + sqrt(3))`

This is the simplified form.