Question

alguem sabe calcular √3/3 . 5√12 . √8/10 . 3√2?

Answer 1

Resposta:

4√3

Explicação passo-a-passo:

$\frac{\sqrt{3}}{3}\cdot \:5\sqrt{1}\cdot \:2\cdot \frac{\sqrt{8}}{10}\cdot \:3\sqrt{2}$

$=\frac{\sqrt{3}}{3}\cdot \:5\cdot \:1\cdot \:2\cdot \frac{\sqrt{8}}{10}\cdot \:3\sqrt{2}\\=\frac{\sqrt{3}}{3}\cdot \:5\cdot \:2\cdot \frac{\sqrt{8}}{10}\cdot \:3\sqrt{2}\\=\frac{\sqrt{3}}{3}\cdot \:30\cdot \frac{\sqrt{8}}{10}\sqrt{2}\\=30\cdot \frac{\sqrt{3}}{3}\cdot \frac{\sqrt{8}}{10}\sqrt{2}\\=30\sqrt{2}\frac{1}{\sqrt{3}}\cdot \frac{\sqrt{8}}{10}$

$=\frac{1\cdot \:2\cdot \:30\sqrt{2}}{\sqrt{3}\sqrt{2}\cdot \:5}\\=\frac{1\cdot \:2\cdot \:30}{\sqrt{3}\cdot \:5}\\=\frac{60}{5\sqrt{3}}\\=\frac{12}{\sqrt{3}}\\=\frac{2^2\cdot \:3}{\sqrt{3}}\\=2^2\sqrt{3}\\=4\sqrt{3}$