| Efectuar: | |
| $\left(\sqrt{18}+\sqrt{8}+\sqrt{2}\right)^2$ | |
| $A)$ | $6\sqrt {2}$ |
| $B)$ | $\sqrt {2}$ |
| $C)$ | $72$ |
| $D)$ | $36$ |
| $E)$ | $12$ |
Solución
| Resolviendo | ||
| Descomponiendo: | ||
| $\left(\sqrt{18}+\sqrt{8}+\sqrt{2}\right)^2$ | ||
| $\left(\sqrt{9 \times 2}+\sqrt{4\times 2}+\sqrt{2}\right)^2$ | ||
| Separando raíces: | ||
| $\left(\sqrt{9}\sqrt{2}+\sqrt{4} \sqrt{2}+\sqrt{2}\right)^2$ | ||
| $\left(3\sqrt{2}+2 \sqrt{2}+\sqrt{2}\right)^2$ | ||
| Factorizando: | ||
| $\left((3+2+1)\sqrt{2}\right)^2$ | ||
| $\left(6\sqrt{2}\right)^2$ | ||
| $6^2\left(\sqrt{2}\right)^2$ | ||
| $36\left(2\right)$ | ||
| $72$ | ||
| Respuesta: | ||
| La solución es la Alternativa C | ||