[tex](-5\sqrt{5}+3y\sqrt{10}+2\sqrt{125}-9y\sqrt{1\frac{1}{9}})\cdot\sqrt{\frac{1}{5}}=\\\\=(-5\sqrt{5}+3\sqrt{10}y+2\sqrt{25\cdot3}-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}\\\\=(-5\sqrt{5}+3\sqrt{10}y+2\cdot5\sqrt{3}-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}=\\\\=(-5\sqrt{5}+3\sqrt{10}y+10\sqrt{3}-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}=(5\sqrt{3}+3\sqrt{10}y-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}=[/tex][tex]=5\sqrt{5}\cdot\sqrt{\frac{1}{5}}+3\sqrt{10}y\cdot\sqrt{\frac{1}{5}}-9\sqrt{\frac{10}{9}}y\cdot\sqrt{\frac{1}{5}}=\\\\=5\sqrt{\not5^1\cdot\frac{1}{\not5_{1}}}+3\sqrt{\not10^2\cdot\frac{1}{\not5_{1}}}y-9\sqrt{\frac{\not10^2}{9}\cdot\frac{1}{\not5_{1}}}y=5\sqrt{1}+3\sqrt{2}y-9\sqrt{\frac{2}{9}}y=\\\\=5\cdot1+3\sqrt{2}y-9\frac{\sqrt{2}}{\sqrt{9}}y=5+3\sqrt{2}y-\not9^3\frac{\sqrt{2}}{\not3_{1}}y=5+3\sqrt{2}y-3\sqrt{2}y=5[/tex]
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[tex](-5\sqrt{5}+3y\sqrt{10}+2\sqrt{125}-9y\sqrt{1\frac{1}{9}})\cdot\sqrt{\frac{1}{5}}=\\\\=(-5\sqrt{5}+3\sqrt{10}y+2\sqrt{25\cdot3}-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}\\\\=(-5\sqrt{5}+3\sqrt{10}y+2\cdot5\sqrt{3}-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}=\\\\=(-5\sqrt{5}+3\sqrt{10}y+10\sqrt{3}-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}=(5\sqrt{3}+3\sqrt{10}y-9\sqrt{\frac{10}{9}}y)\cdot\sqrt{\frac{1}{5}}=[/tex][tex]=5\sqrt{5}\cdot\sqrt{\frac{1}{5}}+3\sqrt{10}y\cdot\sqrt{\frac{1}{5}}-9\sqrt{\frac{10}{9}}y\cdot\sqrt{\frac{1}{5}}=\\\\=5\sqrt{\not5^1\cdot\frac{1}{\not5_{1}}}+3\sqrt{\not10^2\cdot\frac{1}{\not5_{1}}}y-9\sqrt{\frac{\not10^2}{9}\cdot\frac{1}{\not5_{1}}}y=5\sqrt{1}+3\sqrt{2}y-9\sqrt{\frac{2}{9}}y=\\\\=5\cdot1+3\sqrt{2}y-9\frac{\sqrt{2}}{\sqrt{9}}y=5+3\sqrt{2}y-\not9^3\frac{\sqrt{2}}{\not3_{1}}y=5+3\sqrt{2}y-3\sqrt{2}y=5[/tex]