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CAPITULO XXIX

Raíz de un monomio
Ejercicio 213
Hallar las siguientes raíces:
1. $\sqrt{4{a}^{2}{b}^{4}}=±2a{b}^{2}$
2. $\sqrt{25{x}^{6}{y}^{8}}=±5{x}^{3}{y}^{4}$
3. $\sqrt[3]{27{a}^{3}{b}^{9}}=3a{b}^{3}$
4. $\sqrt[3]{–8{a}^{3}{b}^{6}{x}^{12}}=–2a{b}^{2}{x}^{4}$
5. $\sqrt{64{x}^{8}{y}^{10}}=±8{x}^{4}{y}^{5}$
6. $\sqrt[4]{16{a}^{8}{b}^{16}}=±2{a}^{2}{b}^{4}$
7. $\sqrt[5]{{x}^{15}{y}^{20}{z}^{25}}={x}^{3}{y}^{4}{z}^{5}$
8. $\sqrt[3]{–64{a}^{3}{x}^{6}{y}^{18}}=–4a{x}^{2}{y}^{6}$
9. $\sqrt[5]{–243{m}^{5}{n}^{15}}=–3m{n}^{3}$
10. $\sqrt{81{x}^{6}{y}^{8}{z}^{20}}=±9{x}^{3}{y}^{4}{z}^{10}$
11. $\sqrt[3]{1000{x}^{9}{y}^{18}}=10{x}^{3}{y}^{6}$
12. $\sqrt[4]{81{a}^{12}{b}^{24}}=±3{a}^{3}{b}^{6}$
13. $\sqrt[6]{64{a}^{12}{b}^{18}{c}^{30}}=±2{a}^{2}{b}^{3}{c}^{5}$
14. $\sqrt{49{a}^{2n}{b}^{4n}}=±7{a}^{n}{b}^{2n}$
15. $\sqrt[5]{–{x}^{5n}{y}^{10x}}=–{x}^{n}{y}^{2x}$
16. $\sqrt{\frac{9{a}^{2}}{25{x}^{4}}}=\frac{\sqrt{9{a}^{2}}}{\sqrt{25{x}^{4}}}=±\frac{3a}{5{x}^{2}}$
17. $\sqrt[3]{–\frac{27{a}^{3}}{64{x}^{9}}}=–\frac{\sqrt[3]{27{a}^{3}}}{\sqrt[3]{64{x}^{9}}}=–\frac{3a}{4{x}^{3}}$
18. $\sqrt[5]{–\frac{{a}^{5}{b}^{10}}{32{x}^{15}}}=–\frac{\sqrt[5]{{a}^{5}{b}^{10}}}{\sqrt[5]{32{x}^{15}}}=–\frac{a{b}^{2}}{2{x}^{3}}$
19. $\sqrt[4]{\frac{{a}^{8}}{81{b}^{4}{c}^{12}}}=\frac{\sqrt[4]{{a}^{8}}}{\sqrt[4]{81{b}^{4}{c}^{12}}}=±\frac{{a}^{2}}{3b{c}^{3}}$
20. $\sqrt[7]{\frac{128}{{x}^{14}}}=\frac{2}{{x}^{2}}$
21. $\sqrt{\frac{{x}^{2m}}{121{y}^{4n}}}=\frac{\sqrt{{x}^{2m}}}{\sqrt{121{y}^{4n}}}=±\frac{{x}^{m}}{11{y}^{2n}}$
22. $\sqrt[3]{–\frac{125{x}^{9}}{216{m}^{12}}}=–\frac{5{x}^{3}}{6{m}^{4}}$
23. $\sqrt[9]{\frac{{a}^{18}}{{b}^{9}{c}^{27}}}=\frac{\sqrt[9]{{a}^{18}}}{\sqrt[9]{{b}^{9}{c}^{27}}}=\frac{{a}^{2}}{b{c}^{3}}$
24. $\sqrt[10]{\frac{{x}^{20}}{1024{y}^{30}}}=\frac{\sqrt[10]{{x}^{20}}}{\sqrt[10]{1024{y}^{30}}}=±\frac{{x}^{2}}{2{y}^{3}}$