Question

7 simplify the radical. drag your answer into the yellow answer space. \\(\sqrt{32} = \\) 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 32

Descomponer 32 en factores, buscando un cuadrado perfecto: \( 32 = 16 \times 2 \), donde 16 es un cuadrado perfecto (\( 4^2 \)).

Step2: Aplicar propiedad del radical

Usar la propiedad \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (para \( a,b \geq 0 \)): \( \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} \).

Step3: Simplificar la raíz cuadrada

Simplificar \( \sqrt{16} \): \( \sqrt{16} = 4 \), entonces \( \sqrt{32} = 4\sqrt{2} \).

Answer:

\( 4\sqrt{2} \) (el bloque azul con \( 4\sqrt{2} \))