Question

Decomponha os radicando em fatores primos e extraia as seguintes raízes v784

Answer 1

Vamos decompor o radicando em fatores primos, conforme sugere o enunciado:

$\begin{matrix}784&|&2\\392&|&2\\196&|&2\\~~98&|&2\\~~49&|&7\\~~~7&|&7\\~~~1&|&\underline{~~~}\end{matrix}\\\\ ~~~784=2^4\times 7^2$

Então, calculando a raiz quadrada:

$\sqrt{784}=\sqrt{2^4\times 7^2}\\\\ \sqrt{784}=\sqrt{2^4}\times\sqrt{7^2}\\\\ \sqrt{784}=2^2\times7\\\\ \sqrt{784}=4\times7\\\\ \boxed{\sqrt{784}=28}$