Question

Qual é o resultado de
$20 \sqrt{20} \div 5 \sqrt{2}$
​

Answer 1

✅ Após resolver os cálculos, concluímos que o resultado da expressão numérica dada é:

    $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \frac{20\sqrt{20}}{5\sqrt{2}} = 4\sqrt{10}\:\:\:}}\end{gathered} }$

Seja a expressão numérica:

                     $\Large\displaystyle\text{ \begin{gathered} \frac{20\sqrt{20}}{5\sqrt{2}}\end{gathered} }$

Resolvendo a expressão numérica, temos:

     $\Large\displaystyle\text{ \begin{gathered} \frac{20\sqrt{20}}{5\sqrt{2}} = \frac{20\sqrt{20}}{5\sqrt{2}}\cdot\frac{5\sqrt{2}}{5\sqrt{2}} \end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \frac{(20\cdot5)\cdot\sqrt{20\cdot2}}{(5\cdot 5)\cdot\sqrt{2\cdot2}}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \frac{100\sqrt{40}}{25\sqrt{4}}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \frac{100\cdot\sqrt{2^{2}\cdot10}}{25\cdot2}\end{gathered} }$

                       $\Large\displaystyle\text{ \begin{gathered} = \frac{100\cdot2\sqrt{10}}{50}\end{gathered} }$

                       $\Large\displaystyle\text{ \begin{gathered} = \frac{200\sqrt{10}}{50}\end{gathered} }$

                       $\Large\displaystyle\begin{gathered} = 4\sqrt{10}\end{gathered}$

✅ Portanto, o resultado é:

                      $\Large\displaystyle\begin{gathered} 4\sqrt{10}\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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