Question

Calculati 5√3+3{4√2+4[3√3+2(√3-3√2)]:20}-2√2/5 rezultatul fiind 8√3+8√2

Answer 1

[tex]5\sqrt3+3\{4\sqrt{2}+4[3\sqrt{3}+2(\sqrt3-3\sqrt2)]:20\}-\frac{2\sqrt2}{5}=\\ 5\sqrt3+3\{4\sqrt2+4[3\sqrt3+2\sqrt3-6\sqrt2]:20\}-\frac{2\sqrt2}{5}=\\ 5\sqrt3+3\{4\sqrt2+(5\sqrt3-6\sqrt2):5\}-\frac{2\sqrt2}{5}=\\ 5\sqrt{3}+3[4\sqrt2+\sqrt3-\frac{6\sqrt2}{5}]-\frac{2\sqrt2}{5}=\\ 5\sqrt3+3[\sqrt3+\frac{14\sqrt2}{5}]-\frac{2\sqrt2}{5}=\\ 5\sqrt3+3\sqrt3+\frac{42\sqrt2}{5}-\frac{2\sqrt2}{5}=\\ 8\sqrt3+\frac{40\sqrt2}{5}=\bold{8\sqrt3+8\sqrt2}[/tex]