Ответ:
Формулы: [tex]\sqrt[2n]{a^{2n}}=|a|\ \ ,\ \ \sqrt[2n+1]{a^{2n+1}}=a\ \ ,\ \ \sqrt[k]{\dfrac{a^{k}}{b^{k}}}=\dfrac{a}{b}\ \ (k=2n+1)[/tex] .
[tex]1)\ \ 2\sqrt[4]{81}+\sqrt[3]{-125}+\sqrt[6]{1}=2\sqrt[4]{3^4}+\sqrt[3]{(-5)^3}+\sqrt[6]{1^6}=2\cdot 3+(-5)+1=2\\\\\\2)\ \ \sqrt[3]{15\frac{5}{8}}-\sqrt[4]{0,0081}-\dfrac{2}{\sqrt{\dfrac{1}{16}}}=\sqrt[3]{\dfrac{125}{8}}-\sqrt[4]{(0,3)^4}-\dfrac{2}{\sqrt{\dfrac{1}{4^2}}}=\\\\\\=\sqrt[3]{\dfrac{5^3}{2^3}}-0,3-\dfrac{2}{\dfrac{1}{4}}=\dfrac{5}{2}-0,3-8=2,5-0,3-8=-5,8[/tex]
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Ответ:
Формулы: [tex]\sqrt[2n]{a^{2n}}=|a|\ \ ,\ \ \sqrt[2n+1]{a^{2n+1}}=a\ \ ,\ \ \sqrt[k]{\dfrac{a^{k}}{b^{k}}}=\dfrac{a}{b}\ \ (k=2n+1)[/tex] .
[tex]1)\ \ 2\sqrt[4]{81}+\sqrt[3]{-125}+\sqrt[6]{1}=2\sqrt[4]{3^4}+\sqrt[3]{(-5)^3}+\sqrt[6]{1^6}=2\cdot 3+(-5)+1=2\\\\\\2)\ \ \sqrt[3]{15\frac{5}{8}}-\sqrt[4]{0,0081}-\dfrac{2}{\sqrt{\dfrac{1}{16}}}=\sqrt[3]{\dfrac{125}{8}}-\sqrt[4]{(0,3)^4}-\dfrac{2}{\sqrt{\dfrac{1}{4^2}}}=\\\\\\=\sqrt[3]{\dfrac{5^3}{2^3}}-0,3-\dfrac{2}{\dfrac{1}{4}}=\dfrac{5}{2}-0,3-8=2,5-0,3-8=-5,8[/tex]