Question

o valo de
$\sqrt{12} + \sqrt{75} + \sqrt{108}$
equivale a

a)
$10 \sqrt{3}$
b)
$11 \sqrt{3}$
c)
$12 \sqrt{3}$
d)
$13 \sqrt{3}$
​

Answer 1

$\large\boxed{\begin{array}{l}\begin{array}{c|c}\sf108&\sf2\\\sf54&\sf2\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf \sqrt{108}=\sqrt{2^2\cdot3^2\cdot3}=2\cdot3\sqrt{3}=6\sqrt{3}\\\begin{array}{c|c}\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf\sqrt{75}=\sqrt{3\cdot5^2}=5\sqrt{3}\\\begin{array}{c|c}\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt{12}=\sqrt{2^2\cdot3}=2\sqrt{3}\\\sf\sqrt{12}+\sqrt{75}+\sqrt{108}=2\sqrt{3}+5\sqrt{3}+6\sqrt{3}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\sqrt{12}+\sqrt{75}+\sqrt{108}=13\sqrt{3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese\,alternativa\,d}}}}\end{array}}$