Упр.481 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (3v20+7v15-v5):v5; 2) (7^(1/3)-14^(1/3)+56^(1/3)):7^(1/3);
3) 2v(3/2)+v6-3v(2/3); 4) 7v(1 3/4)-v7+0,5v343.

1. $$\frac{3\sqrt{20}+7\sqrt{15}-\sqrt{5}}{\sqrt{5}}=\frac{3\sqrt{20}}{\sqrt{5}}+\frac{7\sqrt{15}}{\sqrt{5}}-\frac{\sqrt{5}}{\sqrt{5}}$$
   $$=3\sqrt{4}+7\sqrt{3}-1=3\cdot 2+7\sqrt{3}-1=5+7\sqrt{3}.$$

2. $$\frac{\sqrt[3]{7}-\sqrt[3]{14}+\sqrt[3]{56}}{\sqrt[3]{7}}=\frac{\sqrt[3]{7}}{\sqrt[3]{7}}-\frac{\sqrt[3]{14}}{\sqrt[3]{7}}+\frac{\sqrt[3]{56}}{\sqrt[3]{7}}$$
   $$=1-\sqrt[3]{2}+\sqrt[3]{8}=1-\sqrt[3]{2}+2=3-\sqrt[3]{2}.$$

3. $$2\sqrt{\frac{3}{2}}+\sqrt{6}-3\sqrt{\frac{2}{3}}=\sqrt{\frac{2^2\cdot 3}{2}}+\sqrt{6}-\sqrt{\frac{3^2\cdot 2}{3}}$$
   $$=\sqrt{6}+\sqrt{6}-\sqrt{6}=\sqrt{6}.$$

4. $$7\sqrt{1\frac{3}{4}}-\sqrt{7}+0{,}5\sqrt{343}=7\sqrt{\frac{4+3}{4}}-\sqrt{7}+0{,}5\sqrt{49\cdot 7}$$
   $$=7\sqrt{\frac{7}{4}}-\sqrt{7}+0{,}5\cdot 7\sqrt{7}=7\cdot \frac{1}{2}\sqrt{7}-\sqrt{7}+3{,}5\sqrt{7}$$
   $$=3{,}5\sqrt{7}-\sqrt{7}+3{,}5\sqrt{7}=6\sqrt{7}.$$

Ответ

1) $$5+7\sqrt{3}$$; 2) $$3-\sqrt[3]{2}$$; 3) $$\sqrt{6}$$; 4) $$6\sqrt{7}$$.