Question

create an expression equivalent to 4√80 in simplest radical form. drag and drop the answer. 5, √50, 8, 40, √4 hint: use ctrl+d to drag the option via keyboard

Explanation:

Step1: Factorizar 800

Descomponemos 800 en factores primos: $800 = 2^{5}\times5^{2}$.

Step2: Reescribir la raíz

$4\sqrt{800}=4\sqrt{2^{5}\times5^{2}}$.

Step3: Aplicar la propiedad $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$4\sqrt{2^{4}\times2\times5^{2}}$.

Step4: Sacar factores fuera de la raíz

$4\times\sqrt{2^{4}}\times\sqrt{5^{2}}\times\sqrt{2}=4\times4\times5\times\sqrt{2}$.

Step5: Calcular el producto

$80\sqrt{2}$.

Answer:

$80\sqrt{2}$