Question

2°) Coloque os radicais abaixo na forma irredutível:
$a) \: \sqrt{50}$
$b) \: \sqrt{112}$
$c) \: \sqrt{27}$
$d ) \: \sqrt{28}$
$e) \: \sqrt{250}$
$f) \: \sqrt{175}$
pfvr me ajudem

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Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\begin{array}{c|c}\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 50=2\cdot5^2\\\sf \sqrt{50}=\sqrt{2\cdot5^2}=5\sqrt{2}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm b)\\\begin{array}{c|c}\sf112&\sf2\\\sf56&\sf2\\\sf28&\sf2\\\sf14&\sf2\\\sf7&\sf7\\\sf1\end{array}\\\sf 112=2^2\cdot2^2\cdot7\\\sf\sqrt{112}=\sqrt{2^2\cdot2^2\cdot7}=2\cdot2\sqrt{7}=4\sqrt{7}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm c)\\\begin{array}{c|c}\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 27=3^2\cdot3\\\sf\sqrt{27}=\sqrt{3^2\cdot3}=3\sqrt{3}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm d)\\\begin{array}{c|c}\sf28&\sf2\\\sf14&\sf2\\\sf7&\sf7\\\sf1\end{array}\\\sf 28=2^2\cdot7\\\sf\sqrt{28}=\sqrt{2^2\cdot7}=2\sqrt{7}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm e)\\\begin{array}{c|c}\sf250&\sf2\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf250=2\cdot5^2\cdot5\\\sf\sqrt{250}=\sqrt{2\cdot5^2\cdot5}=5\sqrt{10}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm f)\\\begin{array}{c|c}\sf175&\sf5\\\sf35&\sf5\\\sf7&\sf7\\\sf1\end{array}\\\sf 175=5^2\cdot7\\\sf\sqrt{175}=\sqrt{5^2\cdot7}=5\sqrt{7}\end{array}}$