Question

Simplificar a expressão ( por meio de fatoração) : raiz de 200 + raiz de 500 + raiz de 8 - raiz de 45???

Answer 1

$<var>\sqrt{200}+\sqrt{500}+\sqrt8-\sqrt{45}=10\sqrt2+\sqrt5+2\sqrt2-3\sqrt5=12\sqrt2+7\sqrt5</var>$

Answer 2

$\sqrt{200} + \sqrt{500} + \sqrt{8} - \sqrt{45} = \\\\ \sqrt{100 \times 2} + \sqrt{100 \times 5} + \sqrt{4 \times 2} - \sqrt{9 \times 5} = \\\\ \sqrt{10^2 \times 2} + \sqrt{10^2 \times 5} + \sqrt{2^2 \times 2} - \sqrt{3^2 \times 5} = \\\\ 10\sqrt{2} + 10\sqrt{5} + 2\sqrt{2} - 3\sqrt{5} = \\\\ \sqrt{2} \times (10 + 2) + \sqrt{5} \times (10 - 3) = \\\\ \boxed{12\sqrt{2} + 7\sqrt{5}}$