(3+√2)^2 Please show work

[tex] \sf \implies {(3 + \sqrt{2} )}^{2} \\ \\ \sf \implies (3 + \sqrt{2} )(3 + \sqrt{2} ) \\ \\ \sf \implies 3(3 + \sqrt{2} ) + \sqrt{2} (3 + \sqrt{2} ) \\ \\ \sf \implies (3 \times 3) + (3 \times \sqrt{2} ) + ( \sqrt{2} \times 3) + ( \sqrt{2} \times \sqrt{2} ) \\ \\ \sf \implies 9 + 3 \sqrt{2} + 3 \sqrt{2} + 2 \\ \\ \sf \implies 9 + 6 \sqrt{2} + 2 \\ \\ \sf \implies 11 + 6 \sqrt{2} [/tex]

drazo18 drazo18 · Answer 2 · 2020-09-09T12:38:55+02:00

Answer:

Exact Form:

[tex]11 +6\sqrt{2}[/tex]

Decimal Form:

19.48528137…

Step-by-step explanation:

Rewrite [tex](3+\sqrt{2} )^2[/tex] as [tex](3+\sqrt{2} )+(3+\sqrt{2} )[/tex]

Expand [tex](3+\sqrt{2} )+(3+\sqrt{2} )[/tex] using the FOIL method.

Apply the distributive property.

[tex]3(3+\sqrt{2} )+\sqrt{2} (3+\sqrt{2} )[/tex]

[tex]3*3 +3+\sqrt{2} +\sqrt{2} (3+\sqrt{2} )[/tex]

[tex]3*3 +3\sqrt{2} +\sqrt{2}* 3+\sqrt{2} \sqrt{2}[/tex]

Simplify and combine like terms.

Simplify each term.

[tex]9+3\sqrt{2} +3\sqrt{2} +2[/tex]

Add 9 and 2

[tex]11+3\sqrt{2} +3\sqrt{2}[/tex]

Add [tex]3\sqrt{2}[/tex] and [tex]3\sqrt{2}[/tex]

11+[tex]6\sqrt{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

11+[tex]6\sqrt{2}[/tex]

and

Decimal Form:

19.48528137

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