Question

Rút gọn các biểu thức sau:

a) \(\sqrt[3]{\left(1-\sqrt{2}\right)^3}\);                  b) \(\sqrt[3]{\left(2\sqrt{2}+1\right)^3}\);                  c) \(\left(\sqrt[3]{\sqrt{2}+1}\right)^3\).

Answer 1

a) \(\sqrt[3]{{{{\left( {1 - \sqrt 2 } \right)}^3}}} = 1 - \sqrt 2 \)

b) \(\sqrt[3]{{{{\left( {2\sqrt 2 + 1} \right)}^3}}} = 2\sqrt 2 + 1\)

c) \({\left( {\sqrt[3]{{\sqrt 2 + 1}}} \right)^3} = \sqrt 2 + 1\)