Question

Simplify:

`(sqrt(7) - sqrt(3))(sqrt(7) + sqrt(3))`

Answer 1

Given: `(sqrt(7) - sqrt(3))(sqrt(7) + sqrt(3))`

Step wise calculation:

This is a product of conjugates of the form (a – b)(a + b) = a² – b².

Here, `a = sqrt(7)` and `b = sqrt(3)`. 

So, `(sqrt(7) - sqrt(3))(sqrt(7) + sqrt(3))` 

= `(sqrt(7))^2 - (\sqrt(3))^2`

= 7 – 3

= 4