Question

Expand (3+√5)(2+√5)

Give your answer in the form a+b√5 where a and b are integers.

Answer 1

11 + 5
`√(5)`

Explanation:

Note that
`√(5)` ×
`√(5)` = 5

Given

(3 +
`√(5)` )(2 +
`√(5)` )

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

3(2 +
`√(5)` ) +
`√(5)`(2 +
`√(5)` ) ← distribute both parenthesis

= 6 + 3
`√(5)` + 2
`√(5)` + 5 ← collect like terms

= 11 + 5
`√(5)` ← in the form a + b
`√(5)`

with a = 11 and b = 5