1.3-bo'lim: Radikallar

1-4-masalalar uchun ifodani eksponensial shaklda yozing.

1. \(\sqrt[7]{y}\) Yechim
2. \(\sqrt[3]{{{x^2}}}\) Yechim
3. \(\sqrt[6]{{ab}}\) Yechim
4. \(\sqrt {{w^2}{v^3}} \) Yechim

5-7-muammolar uchun radikalni baholang.

1. \(\sqrt[4]{{81}}\) Yechim
2. \(\sqrt[3]{{ - 512}}\) Yechim
3. \(\sqrt[3]{{1000}}\) Yechim

8 dan 12 gacha bo'lgan muammolar uchun quyidagilarning har birini soddalashtiring. Faraz qilaylik, x, y va z hammasi musbat.

1. \(\sqrt[3]{{{x^8}}}\) Yechim
2. \(\sqrt {8{y^3}} \) Yechim
3. \(\sqrt[4]{{{x^7}{y^{20}}{z^{11}}}}\) Yechim
4. \(\sqrt[3]{{54{x^6}{y^7}{z^2}}}\) Yechim
5. \(\sqrt[4]{{4{x^3}y}}\,\,\sqrt[4]{{8{x^2}{y^3}{z^5}}}\) Yechim

13 dan 15 gacha bo'lgan muammolar uchun quyidagilarning har birini ko'paytiring. X musbat deb faraz qiling.

1. \(\sqrt x \left( {4 - 3\sqrt x } \right)\) Yechim
2. \(\left( {2\sqrt x + 1} \right)\left( {3 - 4\sqrt x } \right)\) Yechim
3. \(\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)\) Yechim

16-19-masalalar uchun maxrajni ratsionalizatsiya qiling. Faraz qilaylik, x va y ikkalasi ham musbat.

1. \(\displaystyle \frac{6}{{\sqrt x }}\) Yechim
2. \(\displaystyle \frac{9}{{\sqrt[3]{{2x}}}}\) Yechim
3. \(\displaystyle \frac{4}{{\sqrt x + 2\sqrt y }}\) Yechim
4. \(\displaystyle \frac{{10}}{{3 - 5\sqrt x }}\) Yechim