2 [latex] \sqrt{20} [/latex]-3 [latex] \sqrt{45} [/latex]+[latex] \sqrt{18} [/latex]+[latex] \sqrt{72} [/latex]-[latex] \sqrt{80} [/latex]

Question

2 [latex] \sqrt{20} [/latex]-3 [latex] \sqrt{45} [/latex]+[latex] \sqrt{18} [/latex]+[latex] \sqrt{72} [/latex]-[latex] \sqrt{80} [/latex]

Гость

Ответ(ы) на вопрос:

Accepted Answer

[latex]2\sqrt{20}-3\sqrt{45}+\sqrt{18}+\sqrt{72}-\sqrt{80}=\\=2\sqrt{4\cdot5}-3\sqrt{5\cdot9}+\sqrt{2\cdot9}+\sqrt{2\cdot36}-\sqrt{5\cdot16}=\\=4\sqrt5-9\sqrt5+3\sqrt2+6\sqrt2-4\sqrt5=9\sqrt2-9\sqrt5=9\cdot\left(\sqrt2-\sqrt5\right)[/latex]