Question

`(3 + \sqrt[]{2} ) {}^(2)`
​

Answer 1

11 + 6
`√(2)`

Explanation:

(3 +
`√(2)` )²

= (3 +
`√(2)` )( 3 +
`√(2)` )

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

= 3( 3 +
`√(2)` ) +
`√(2)` ( 3 +
`√(2)` )

Distribute each parenthesis noting that
`√(2)` ×
`√(2)` = 2

= 9 + 3
`√(2)` + 3
`√(2)` + 2 ← collect like terms

= 11 + 6
`√(2)`