1.3-bo'lim : Radikallar
8. Quyidagi ifodani soddalashtiring. \(x\) ijobiy deb faraz qiling.
\[\sqrt[3]{{{x^8}}}\]Yechim
Eslatib o'tamiz, soddalashtirish orqali biz ifodani soddalashtirilgan radikal shaklga qo'yishni xohlaymiz (buni biz ushbu bo'lim uchun eslatmalarda aniqlaganmiz).
Buning uchun bu ifoda uchun radikalni quyidagicha yozishimiz kerak:
\[{x^8} = {x^6}{x^2} = {\left( {{x^2}} \right)^3}{x^2}\]2-qadam
Endi biz radikalni qayta yozganimizdan so'ng, radikal bilan kurashish va ifodani soddalashtirilgan radikal shaklda olish oson.
\[\sqrt[3]{{{x^8}}} = \sqrt[3]{{{{\left( {{x^2}} \right)}^3}{x^2}}} = \sqrt[3]{{{{\left( {{x^2}} \right)}^3}}}\sqrt[3]{{{x^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{{x^2}\,\,\sqrt[3]{{{x^2}}}}}\]