Question

A ordem correta da simplificação de,

√48 , √12 e √50 é?

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Answer 1

$\large\boxed{\begin{array}{l}\begin{array}{c|l}\sf48&\sf2&\sf24&\sf2\\\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf 4 8=2^4\cdot3=(2^2)^2\cdot3\\\sf\sqrt{48}=\sqrt{(2^2)^2\cdot3}=2^2\sqrt{3}=4\sqrt{3}\\\sf 12=2^2\cdot3\\\sf\sqrt{12}=\sqrt{2^2\cdot3}=2\sqrt{3}\\\begin{array}{c|l}\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 25=2\cdot5^2\\\sf\sqrt{50}=\sqrt{2\cdot5^2}=5\sqrt{2}\end{array}}$