Question

How do you simplify `(3+sqrt 5)(3-sqrt 5)`?

Answer 1

`(3+sqrt 5)(3-sqrt 5)=4`

Explanation:

`(3+sqrt 5)(3-sqrt 5)`

This is an example of the difference of squares, `(a^2-b^2)=(a+b)(a-b)`, where `a=3 and b=sqrt5`.

`(3^2-sqrt(5^2))=`

`9-sqrt(5^2)`

Apply the square root rule `sqrt(x^2)=x`.

`9-5=4`