√6-4√2+√7+2√10+2-√[4](-5)^2 ni hisoblang.

Dastlab $\sqrt{6-4\sqrt{2}}$, $\sqrt{7+2\sqrt{10}}$ va $\sqrt[4]{(-5)^2}$ ifodalarni soddalashtirib olamiz. 1) $\sqrt{6-4\sqrt{2}}=\sqrt{\left(2-\sqrt{2}\right)^2}=\left|2-\sqrt{2}\right|=2-\sqrt{2}$, 2) $\sqrt{7+2\sqrt{10}}=\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}=\sqrt{5}+\sqrt{2}$ va 3) $\sqrt[4]{(-5)^2}=\sqrt[4]{25}=\sqrt{5}$. Bu natijalardan foydalanib berilgan ifodaning qiymatini hisoblaymiz, ya’ni: $\sqrt{6-4\sqrt{2}}+\sqrt{7+2\sqrt{10}}+2-\sqrt[4]{(-5)^2}=2-\sqrt{2}+\sqrt{5}+\sqrt{2}+2-\sqrt{5}=2+2=4$.

Manba: UZBMB namunaviy test topshiriqlari (2021, mutaxassislik). Sh.A.Alimov, O.R.Xolmuhamedov, M.A.Mirzaahmedov. Algebra, umumiy o‘rta ta’lim maktablarining 8-sinfi uchun darslik. “O‘qituvchi” nashriyot-matbaa ijodiy uyi. Toshkent−2019