Question

simplificar \\(\sqrt{108}\\)

options:

• \\(8\sqrt{2}\\)
• \\(6\sqrt{3}\\)
• \\(10\sqrt{8}\\)
• \\(2\sqrt{27}\\)

Explanation:

Factorizar el número bajo el radical

$$ 108 = 36 \times 3 = 6^2 \times 3 $$

Aplicar la propiedad de los radicales

$$ \sqrt{108} = \sqrt{6^2 \times 3} = \sqrt{6^2} \times \sqrt{3} = 6\sqrt{3} $$

Answer:

• (A) \(8\sqrt{2}\)
• (B) \(6\sqrt{3}\) (Correct answer)
• (C) \(10\sqrt{8}\)
• (D) \(2\sqrt{27}\)