Question

Expand and simplify (2+sqrt(5))(1+sqrt(5)) give answers in form of a b c where a b c are integers

Answer 1

7 + 3
`√(5)`

Explanation:

Given

(2 +
`√(5)` )(1 +
`√(5)` )

Each term in the second factor is multiplied by each term in the first factor, that is

2(1 +
`√(5)` ) +
`√(5)`(1 +
`√(5)`)

Distribute both parenthesis noting that
`√(5)` ×
`√(5)` = 5

= 2 + 2
`√(5)` +
`√(5)` + 5 ( collect like terms )

= 7 + 3
`√(5)`