Question

fatore:
$\sqrt{12}$
$\sqrt{50}$
$\sqrt{18}$
$\sqrt{27}$
$\sqrt{144}$
​

Answer 1

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$\LARGE\boxed{\begin{array}{l}\begin{array}{r|l}\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt{12}=\sqrt{2^2\cdot3}\\\sf\sqrt{12}=2\sqrt{3}\end{array}}$

$\LARGE\boxed{\begin{array}{l}\begin{array}{r|l}\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf\sqrt{50}=\sqrt{2\cdot5^2}\\\sf\sqrt{50}=5\sqrt{2}\end{array}}$

$\LARGE\boxed{\begin{array}{l}\begin{array}{r|l}\sf18&\sf2\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt{18}=\sqrt{2\cdot3^2}\\\sf\sqrt{18}=3\sqrt{2}\end{array}}$

$\LARGE\boxed{\begin{array}{l}\begin{array}{r|l}\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt{27}=\sqrt{3^2\cdot3}\\\sf\sqrt{27}=3\sqrt{3}\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{r|l}\sf144&\sf2\\\sf72&\sf2\\\sf36&\sf2\\\sf18&\sf2\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt{144}=\sqrt{2^2\cdot2^2\cdot3^2}\\\sf\sqrt{144}=2\cdot2\cdot3\\\sf\sqrt{144}=12\end{array}}$