Question

Simplifique o radical: 1128a²b3 = ?



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Answer 1

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$\sf\sqrt{1128a^2b^3}\\\begin{array}{c|l}\sf1128&\sf2\\\sf564&\sf2\\\sf282&\sf2\\\sf141&\sf3\\\sf47&\sf47\\\sf1\end{array}\\\sf 1128=2^2\cdot2\cdot3\cdot47\\\sf\sqrt{1128a^2b^3}=\sqrt{2^{\diagdown\!\!\!\!2}\cdot2\cdot3\cdot47\cdot a^{\diagdown\!\!\!\!2}\cdot b^{\diagdown\!\!\!\!2}\cdot b}\\\sf\sqrt{1128a^2b^3}=2ab\sqrt{282b}\checkmark$