Question

8 simplify the radical. drag your answer into the yellow answer space. \\(\sqrt{54} = \\) yellow answer space options: \\(3\sqrt{6}\\), \\(2\sqrt{5}\\), \\(25\sqrt{5}\\), \\(4\sqrt{2}\\), \\(6\sqrt{3}\\), \\(2\sqrt{4}\\), \\(5\sqrt{3}\\), \\(3\sqrt{3}\\), \\(7\sqrt{2}\\), \\(9\sqrt{6}\\)

Explanation:

Step1: Factorizar 54

Descomponemos 54 en factores: \( 54 = 9 \times 6 \)

Step2: Aplicar propiedad del radical

Usamos \( \sqrt{ab} = \sqrt{a}\sqrt{b} \) ( \( a,b \geq 0 \) ), así que \( \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} \)

Step3: Simplificar \( \sqrt{9} \)

Como \( \sqrt{9} = 3 \), entonces \( \sqrt{54} = 3\sqrt{6} \)

Answer:

\( 3\sqrt{6} \) (la opción de color rosa con texto \( 3\sqrt{6} \))