Question

Resolva:

$\sqrt{91 + \sqrt{76 + \sqrt{21 + \sqrt{14 + \sqrt{4} } } } }$

Passo-a-passo:
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Answer 1

$\displaystyle \sf \sqrt{91+\sqrt{76+\sqrt{21+\sqrt{14+\sqrt{4}}}}} \\\\\\ \sqrt{91+\sqrt{76+\sqrt{21+\sqrt{14+2}}}} \\\\\\ \sqrt{91+\sqrt{76+\sqrt{21+\sqrt{16}}}} \\\\ \sqrt{91+\sqrt{76+\sqrt{21+4}}} \\\\ \sqrt{91+\sqrt{76+\sqrt{25}}} \\\\ \sqrt{91+\sqrt{76+5}} \\\\ \sqrt{91+\sqrt{81}} \\\\ \sqrt{91+9} \\\\ \sqrt{100} \\\\ 10 \\\\ portanto : \\\\ \sqrt{91+\sqrt{76+\sqrt{21+\sqrt{14+\sqrt{4}}}}} = 10$

Answer 2

$\Large\displaystyle\text{ \begin{gathered}\sf\boxed{\boxed{ \sf{ \sqrt{91 + \sqrt{76 + \sqrt{21 + \sqrt{14 + \sqrt{4} } }}}=10}}} \checkmark\end{gathered} }$

• Explicação:

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \sqrt{76 + \sqrt{21 + \sqrt{14 + \underbrace{\sqrt{4}}_{2} } } } } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \sqrt{76 + \sqrt{21 + \sqrt{14 + 2} } } } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \sqrt{76 + \sqrt{21 + \underbrace{\sqrt{16}} _{4} } } } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \sqrt{76 + \sqrt{21 + 4} } } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \sqrt{76 + \underbrace{ \sqrt{25}} _{5} } } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \sqrt{76 + 5} } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + \underbrace{\sqrt{81}} _{9} } } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \sqrt{91 + 9} } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ \underbrace{ \sqrt{100}} _{10} } \end{gathered} }$

$\Large\displaystyle\begin{gathered} \sf{ 10 \: \checkmark } \end{gathered}$