Question

1- √200 simplificandoa raiz ao lado , obtém-se:
2- raiz qubica de 1080 simplificando a raiz ao lado , obtém-se

Answer 1

$\sqrt{200}$
$\frac{200}{2} = 100 \\ \frac{100}{2} = 50 \\ \frac{50}{2} = 25 \\ \frac{25}{5} = 5 \\ \frac{5}{5} = 1$
$200 = {2}^{3} \times {5}^{2} \\ \sqrt{200} = 5 \times 2 \sqrt{2} \\ \sqrt{200} = 10 \sqrt{2}$

$\sqrt[3]{1080}$
$\frac{1080}{2} = 540 \\ \frac{540}{2} = 270 \\ \frac{270}{2} = 135 \\ \frac{135}{3} = 45 \\ \frac{45}{3} = 15 \\ \frac{15}{3} \\ \frac{5}{5} = 1$
$1080 = {2}^{3} \times {3}^{3} \times 5 \\ \sqrt[3]{1080} = 2 \times 3 \times \sqrt[3]{5} \\ \sqrt[3]{1080} = 6 \sqrt[3]{5}$