3) √10-2√21; 5) 17+ 12√2; 4) √6-2√5; 6) √28-16√3. Освободитесь от иррациональности в знаменателе (1.106- 106. 1) 2 √6 5 4); 125' 6 7) 54/32 6 2 √3 4 5)-: 9 8) 4/64 4 48 6)-24/3: 3 9) 70/81

1) \[\frac{2}{\sqrt{6}} = \frac{2 \cdot \sqrt{6}}{\sqrt{6} \cdot \sqrt{6}} = \frac{2\sqrt{6}}{6} = \frac{\sqrt{6}}{3}\]

2) \[\frac{6}{\sqrt{3}} = \frac{6 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}\]

3) \[\frac{4}{\sqrt[4]{8}} = \frac{4}{\sqrt[4]{2^3}} = \frac{4 \cdot \sqrt[4]{2}}{\sqrt[4]{2^3} \cdot \sqrt[4]{2}} = \frac{4\sqrt[4]{2}}{\sqrt[4]{2^4}} = \frac{4\sqrt[4]{2}}{2} = 2\sqrt[4]{2}\]

4) \[\frac{5}{\sqrt[6]{125}} = \frac{5}{\sqrt[6]{5^3}} = \frac{5}{\sqrt{\sqrt[3]{5^3}}} = \frac{5}{\sqrt{5}} = \frac{5 \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{5\sqrt{5}}{5} = \sqrt{5}\]

5) \[-\frac{4}{\sqrt[9]{12}} = -\frac{4}{\sqrt[9]{2^2 \cdot 3}} = -\frac{4 \cdot \sqrt[9]{2^7 \cdot 3^8}}{\sqrt[9]{2^2 \cdot 3} \cdot \sqrt[9]{2^7 \cdot 3^8}} = -\frac{4\sqrt[9]{2^7 \cdot 3^8}}{\sqrt[9]{2^9 \cdot 3^9}} = -\frac{4\sqrt[9]{2^7 \cdot 3^8}}{2 \cdot 3} = -\frac{4\sqrt[9]{2^7 \cdot 3^8}}{6} = -\frac{2\sqrt[9]{2^7 \cdot 3^8}}{3}\]

6) \[-\frac{24}{\sqrt[3]{3}} = -\frac{24 \cdot \sqrt[3]{3^2}}{\sqrt[3]{3} \cdot \sqrt[3]{3^2}} = -\frac{24\sqrt[3]{9}}{\sqrt[3]{3^3}} = -\frac{24\sqrt[3]{9}}{3} = -8\sqrt[3]{9}\]

7) \[\frac{54}{\sqrt[6]{32}} = \frac{54}{\sqrt[6]{2^5}} = \frac{54 \cdot \sqrt[6]{2}}{\sqrt[6]{2^5} \cdot \sqrt[6]{2}} = \frac{54\sqrt[6]{2}}{\sqrt[6]{2^6}} = \frac{54\sqrt[6]{2}}{2} = 27\sqrt[6]{2}\]

8) \[\frac{4}{\sqrt[9]{64}} = \frac{4}{\sqrt[9]{2^6}} = \frac{4}{\sqrt[3]{\sqrt[3]{2^6}}} = \frac{4}{\sqrt[3]{2^2}} = \frac{4}{\sqrt[3]{4}} = \frac{4 \cdot \sqrt[3]{2}}{\sqrt[3]{4} \cdot \sqrt[3]{2}} = \frac{4\sqrt[3]{2}}{\sqrt[3]{8}} = \frac{4\sqrt[3]{2}}{2} = 2\sqrt[3]{2}\]

9) \[\frac{76}{\sqrt[3]{81}} = \frac{76}{\sqrt[3]{3^4}} = \frac{76}{\sqrt[3]{3^3 \cdot 3}} = \frac{76}{3\sqrt[3]{3}} = \frac{76 \cdot \sqrt[3]{3^2}}{3\sqrt[3]{3} \cdot \sqrt[3]{3^2}} = \frac{76\sqrt[3]{9}}{3\sqrt[3]{3^3}} = \frac{76\sqrt[3]{9}}{3 \cdot 3} = \frac{76\sqrt[3]{9}}{9}\]