Question

Write (5-√5) (5-√5) in the form a+b√5, where a and b are integers.

Answer 1

30 - 10
`√(5)`

Explanation:

(5 -
`√(5)` )(5 -
`√(5)` )

each term in the second factor is multiplied by each term in the first factor.

5(5 -
`√(5)` ) -
`√(5)` (5 -
`√(5)` ) ← distribute both parenthesis

= 25 - 5
`√(5)` - 5
`√(5)` + 5 ← collect like terms

= 30 - 10
`√(5)`