Question

state whether irrational (2+√2)² and why?​

Answer 1

$\large{\huge{\underline \mathbb{ \overline { \mid{ \blue{Answer} \mid}}}} } \\ \\ (2 + \sqrt{2} ) {}^{2} \\ \\ 2 {}^{2} + (\sqrt{2}) {}^{2} + 2(2)( \sqrt{2} ) \\ \\ 4 + 2 + 4 \sqrt{2} \\ \\ as \: \sqrt{2 } \: is \: irrational \: so \\ \:( 2 + \sqrt{2} ) {}^{2} \: is \: also \: irrational.$

Answer 2

Answer:

$\begin{gathered} \large{\huge{\underline \mathbb{ \overline { \mid{ \blue{Answer} \mid}}}} } \\ \\ (2 + \sqrt{2} ) {}^{2} \\ \\ 2 {}^{2} + (\sqrt{2}) {}^{2} + 2(2)( \sqrt{2} ) \\ \\ 4 + 2 + 4 \sqrt{2} \\ \\ as \: \sqrt{2 } \: is \: irrational \: so \\ \:( 2 + \sqrt{2} ) {}^{2} \: is \: also \: irrational.\end{gathered}$