Asosiy tarkibga o'tish

1.3-bo'lim : Radikallar

1-6-masalalar uchun ifodani eksponensial shaklda yozing.

  1. \(\sqrt {3n} \)
  2. \(\sqrt[6]{{2y}}\)
  3. \(\sqrt[5]{{7{x^3}}}\)
  4. \(\sqrt[4]{{xyz}}\)
  5. \(\sqrt {x + y} \)
  6. \(\sqrt[3]{{{a^3} + {b^3}}}\)

7-12 muammolar uchun radikalni baholang.

  1. \(\sqrt {256} \)
  2. \(\sqrt[4]{{256}}\)
  3. \(\sqrt[8]{{256}}\)
  4. \(\sqrt[5]{{ - 1024}}\)
  5. \(\sqrt[3]{{ - 216}}\)
  6. \(\sqrt[3]{{343}}\)

13-22-muammolar uchun quyidagilarning har birini soddalashtiring. \(x\), \(y\) va \(z\) hammasi ijobiy deb faraz qiling.

  1. \(\sqrt {{z^5}} \)
  2. \(\sqrt[3]{{{z^5}}}\)
  3. \(\sqrt[3]{{16{x^{17}}}}\)
  4. \(\sqrt[6]{{128{y^{11}}}}\)
  5. \(\sqrt {{x^3}{y^{17}}{z^4}} \)
  6. \(\sqrt[4]{{{x^3}{y^{20}}{z^5}}}\)
  7. \(\sqrt[4]{{729{x^7}y\,{z^{13}}}}\)
  8. \(\sqrt[3]{{4{x^2}y}}\,\,\,\sqrt[3]{{10{x^5}{y^2}}}\)
  9. \(\sqrt {3x} \,\,\sqrt {6x} \,\,\sqrt {14x} \)
  10. \(\sqrt[4]{{2x{y^3}}}\,\,\,\sqrt[4]{{32{x^2}{y^2}}}\)

23 dan 26 gacha bo'lgan muammolar uchun quyidagi raqamlarning har birini ko'paytiring. \(x\) ijobiy deb faraz qiling.

  1. \(\left( {2\sqrt x + 4} \right)\left( {\sqrt x - 7} \right)\)
  2. \(\sqrt[3]{x}\left( {\sqrt[3]{x} + 2\sqrt[3]{{{x^4}}}} \right)\)
  3. \(\left( {\sqrt x + \sqrt {2y} } \right)\left( {\sqrt x - \sqrt {2y} } \right)\)
  4. \({\left( {\sqrt[4]{x} + \sqrt[4]{{{x^2}}}} \right)^2}\)

27-35-masalalar uchun maxrajni ratsionalizatsiya qiling. \(x\) va \(y\) ikkalasi ham ijobiy deb faraz qiling.

  1. \(\displaystyle \frac{9}{{\sqrt y }}\)
  2. \(\displaystyle \frac{3}{{\sqrt {7x} }}\)
  3. \(\displaystyle \frac{1}{{\sqrt[4]{x}}}\)
  4. \(\displaystyle \frac{{12}}{{\sqrt[5]{{3{x^2}}}}}\)
  5. \(\displaystyle \frac{2}{{4 - \sqrt x }}\)
  6. \(\displaystyle \frac{9}{{\sqrt {3y} + 2}}\)
  7. \(\displaystyle \frac{4}{{\sqrt 7 - 6\sqrt x }}\)
  8. \(\displaystyle \frac{{ - 6}}{{\sqrt {5x} + 10\sqrt y }}\)
  9. \(\displaystyle \frac{{4 + x}}{{x - \sqrt x }}\)

36-38 muammolar uchun bayonotning to'g'ri yoki noto'g'ri ekanligini aniqlang. Agar noto'g'ri bo'lsa, nima uchun noto'g'ri ekanligini tushuntiring.

  1. \(3{x^{\frac{1}{2}}} = \sqrt {3x} \)
  2. \(\sqrt[3]{{x + 6}} = \sqrt[3]{x} + \sqrt[3]{6}\)
  3. \(\sqrt[4]{{{x^2}}} = \sqrt x \)
  4. Yuqoridagi 13-35 muammolar uchun biz har doim o'zgaruvchilar ijobiy deb taxmin qilish uchun ko'rsatma qo'shdik. Nima uchun bu ko'rsatma qo'shilgan? Agar bizda bunday ko'rsatma bo'lmasa, muammolarga javoblar qanday o'zgaradi?