33.6 a) √0,125; 6) √0,0625; B) √0,0081; г) √0,027,

Задание 33.6.

а) $$ \sqrt{0,125} = \sqrt{\frac{125}{1000}} = \sqrt{\frac{1}{8}} = \frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}}$$.

б) $$ \sqrt[6]{0,0625} = \sqrt[6]{\frac{625}{10000}} = \sqrt[6]{\frac{5^4}{10^4}} = \sqrt[6]{\left(\frac{5}{10}\right)^4} = \sqrt[6]{\left(\frac{1}{2}\right)^4} = \sqrt[6]{\frac{1}{16}} $$.

в) $$ \sqrt[6]{0,0081} = \sqrt[6]{\frac{81}{10000}} $$.

г) $$ \sqrt[6]{0,027} = \sqrt[6]{\frac{27}{1000}} = \sqrt[6]{\frac{3^3}{10^3}} = \sqrt[6]{\left(\frac{3}{10}\right)^3} = \sqrt{\frac{3}{10}} $$.

Ответ: а) $$ \frac{1}{2\sqrt{2}}$$; б) $$ \sqrt[6]{\frac{1}{16}} $$; в) $$ \sqrt[6]{\frac{81}{10000}} $$; г) $$ \sqrt{\frac{3}{10}} $$.