Question

\sqrt[]{2} ) {}^{2} " alt="(3 + \sqrt[]{2} ) {}^{2} " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

11 + 6$\sqrt{2}$

Step-by-step explanation:

(3 + $\sqrt{2}$ )²

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

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

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

Distribute each parenthesis noting that $\sqrt{2}$ × $\sqrt{2}$ = 2

= 9 + 3$\sqrt{2}$ + 3$\sqrt{2}$ + 2 ← collect like terms

= 11 + 6$\sqrt{2}$