1.3-bo'lim : Radikallar
10. Quyidagi ifodani soddalashtiring. \(x\), \(y\) va \(z\) ijobiy deb faraz qiling.
\[\sqrt[4]{{{x^7}{y^{20}}{z^{11}}}}\]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:
\[{x^7}{y^{20}}{z^{11}} = {x^4}{y^{20}}{z^8}{x^3}{z^3} = {x^4}{\left( {{y^5}} \right)^4}{\left( {{z^2}} \right)^4}{x^3}{z^3}\]2-qadam
Endi biz radikalni qayta yozganimizdan so'ng, radikal bilan kurashish va ifodani soddalashtirilgan radikal shaklda olish oson.
\[\sqrt[4]{{{x^7}{y^{20}}{z^{11}}}} = \sqrt[4]{{{x^4}{{\left( {{y^5}} \right)}^4}{{\left( {{z^2}} \right)}^4}{x^3}{z^3}}} = \sqrt[4]{{{x^4}{{\left( {{y^5}} \right)}^4}{{\left( {{z^2}} \right)}^4}}}\,\,\,\sqrt[4]{{{x^3}{z^3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{x\,{y^5}{z^2}\,\,\sqrt[4]{{{x^3}{z^3}}}}}\]