✅ Após resolver os cálculos, concluímos que o resultado da expressão numérica dada é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf \frac{20\sqrt{20}}{5\sqrt{2}} = 4\sqrt{10}\:\:\:}}\end{gathered}$}[/tex]
Seja a expressão numérica:
[tex]\Large\displaystyle\text{$\begin{gathered} \frac{20\sqrt{20}}{5\sqrt{2}}\end{gathered}$}[/tex]
Resolvendo a expressão numérica, temos:
[tex]\Large\displaystyle\text{$\begin{gathered} \frac{20\sqrt{20}}{5\sqrt{2}} = \frac{20\sqrt{20}}{5\sqrt{2}}\cdot\frac{5\sqrt{2}}{5\sqrt{2}} \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{(20\cdot5)\cdot\sqrt{20\cdot2}}{(5\cdot 5)\cdot\sqrt{2\cdot2}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{100\sqrt{40}}{25\sqrt{4}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{100\cdot\sqrt{2^{2}\cdot10}}{25\cdot2}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{100\cdot2\sqrt{10}}{50}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{200\sqrt{10}}{50}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 4\sqrt{10}\end{gathered}$}[/tex]
✅ Portanto, o resultado é:
[tex]\Large\displaystyle\text{$\begin{gathered} 4\sqrt{10}\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
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