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\begin{center}\section*{\textcolor{red}{AP2 sur les racines carrées }}\end{center}



\subsection{}
\noindent Calculer : 
\begin{enumerate}[$a=$]
\item $\sqrt{9}=3$ car $3\geqslant 0$ et $3^2=9$

\item $\sqrt{25}=5$ car $5\geqslant 0$ et $5^2=25$

\item $\sqrt{0}=0$ car $0\geqslant 0$ et $0^2=0$

\item $\sqrt{1}=1$ car $1\geqslant 0$ et $1^2=1$

\item $\sqrt{(-3)^2}=\sqrt{9}=3$

\item $\sqrt{2}$ na pas d'autre écriture possible.

\end{enumerate}


\subsection{}
\noindent Calculer : 

\begin{enumerate}[$A=~$]
\item $\sqrt{2}\times \sqrt{18}=\sqrt{3^2\times 2}=\boxed{\textcolor{red}{3\sqrt{2}}}$

\item $\sqrt{3}\times \sqrt{27}=\sqrt{3^2\times 3}=\boxed{\textcolor{red}{3\sqrt{3}}}$

\item $\dfrac{\sqrt{54}}{\sqrt{6}}=\sqrt{\sqrt{54}}6=\sqrt{9}=\boxed{\textcolor{red}{3}}$

\end{enumerate}


\subsection{}

\noindent Simplifier : 

\begin{enumerate}[$A=~$]
\item $\sqrt{50}=\sqrt{25\times 2}=\sqrt{5^2\times 2}=\boxed{\textcolor{red}{5\sqrt{2}}}$

\item $\sqrt{8}=\sqrt{2^2\times 2}=\boxed{\textcolor{red}{2\sqrt{2}}}$

\item $\sqrt{32}=\sqrt{16\times 2=\sqrt{4^2\times 2}}=\boxed{\textcolor{red}{4\sqrt{2}}}$

\item $\sqrt{48}=\sqrt{1re 6\times 3}=\sqrt{4^2\times 3}=\boxed{\textcolor{red}{4\sqrt{3}}}$

\item $\sqrt{3}\times \sqrt{6}=\sqrt{3}\times \sqrt{2}\times \sqrt{3}=\sqrt{3}^2\times \sqrt{2}=\boxed{\textcolor{red}{3\sqrt{2}}}$

\item $\sqrt{5}\times \sqrt{20}=\sqrt{5}\times \sqrt{2^2\times 5}=\sqrt{5}\times 2\sqrt{5}=\sqrt{5}^2\times 2=\boxed{\textcolor{red}{10}}$

\item $\sqrt{3}\times \sqrt{6}\times \sqrt{8}=\sqrt{3}\times \sqrt{2}\times \sqrt{3}\times 2\sqrt{2}=2\times 2\times 3=\boxed{\textcolor{red}{12}}$

\end{enumerate}

\subsection{}
\noindent Simplifier :

\begin{enumerate}[$A=~$]
\item $2\sqrt{20}-\sqrt{45}+\sqrt{125}=2\times 2\sqrt{5}-3\sqrt{5}+5\sqrt{5}=(4-3+5)\sqrt{5}=\boxed{\textcolor{red}{6\sqrt{5}}}$

\item $7\sqrt{3}-3\sqrt{48}+5\sqrt{12}=7\sqrt{3}-3\times 4\sqrt{3}+5\times 2\sqrt{3}=(7-12+10)\sqrt{3}=\boxed{\textcolor{red}{5\sqrt{3}}}$
\end{enumerate}



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