Question

(3+√2)^2 Please show work

Answer 1

Answer:

$\boxed{\sf {(3+\sqrt{2})}^2 = 11 + 6 \sqrt{2} }$

Step-by-step explanation:

$\sf \implies {(3 + \sqrt{2} )}^{2} \\ \\ \sf \implies (3 + \sqrt{2} )(3 + \sqrt{2} ) \\ \\ \sf \implies 3(3 + \sqrt{2} ) + \sqrt{2} (3 + \sqrt{2} ) \\ \\ \sf \implies (3 \times 3) + (3 \times \sqrt{2} ) + ( \sqrt{2} \times 3) + ( \sqrt{2} \times \sqrt{2} ) \\ \\ \sf \implies 9 + 3 \sqrt{2} + 3 \sqrt{2} + 2 \\ \\ \sf \implies 9 + 6 \sqrt{2} + 2 \\ \\ \sf \implies 11 + 6 \sqrt{2}$

Answer 2

Answer:

Exact Form:

$11 +6\sqrt{2}$

Decimal Form:

19.48528137…

Step-by-step explanation:

Rewrite $(3+\sqrt{2} )^2$ as $(3+\sqrt{2} )+(3+\sqrt{2} )$

Expand $(3+\sqrt{2} )+(3+\sqrt{2} )$ using the FOIL method.

Apply the distributive property.

    $3(3+\sqrt{2} )+\sqrt{2} (3+\sqrt{2} )$

    $3*3 +3+\sqrt{2} +\sqrt{2} (3+\sqrt{2} )$

    $3*3 +3\sqrt{2} +\sqrt{2}* 3+\sqrt{2} \sqrt{2}$

Simplify and combine like terms.

       Simplify each term.

        $9+3\sqrt{2} +3\sqrt{2} +2$

         Add 9 and 2

         $11+3\sqrt{2} +3\sqrt{2}$

         Add $3\sqrt{2}$ and $3\sqrt{2}$

          11+$6\sqrt{2}$  

The result can be shown in multiple forms.

Exact Form:

 11+$6\sqrt{2}$  

and

Decimal Form:

19.48528137

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