Question

(3+√2)^2 Please show work

Answer 1

Exact Form:

`11 +6√(2)`

Decimal Form:

19.48528137…

Explanation:

Rewrite
`(3+√(2) )^2` as
`(3+√(2) )+(3+√(2) )`

Expand
`(3+√(2) )+(3+√(2) )` using the FOIL method.

Apply the distributive property.

`3(3+√(2) )+√(2) (3+√(2) )`

`3*3 +3+√(2) +√(2) (3+√(2) )`

`3*3 +3√(2) +√(2)* 3+√(2) √(2)`

Simplify and combine like terms.

Simplify each term.

`9+3√(2) +3√(2) +2`

Add 9 and 2

`11+3√(2) +3√(2)`

Add
`3√(2)` and
`3√(2)`

11+
`6√(2)`

The result can be shown in multiple forms.

Exact Form:

11+
`6√(2)`

and

Decimal Form:

19.48528137

....

Answer 2

`\boxed{\sf {(3+√(2))}^2 = 11 + 6 √(2) }`

Explanation:

`\sf \implies {(3 + √(2) )}^(2) \\ \\ \sf \implies (3 + √(2) )(3 + √(2) ) \\ \\ \sf \implies 3(3 + √(2) ) + √(2) (3 + √(2) ) \\ \\ \sf \implies (3 * 3) + (3 * √(2) ) + ( √(2) * 3) + ( √(2) * √(2) ) \\ \\ \sf \implies 9 + 3 √(2) + 3 √(2) + 2 \\ \\ \sf \implies 9 + 6 √(2) + 2 \\ \\ \sf \implies 11 + 6 √(2)`