Đáp án:
b) 1
Giải thích các bước giải:
\(\begin{array}{l}
b)\sqrt[4]{{9 + 2.3.2\sqrt 2 + 8}} - \sqrt 2 \\
= \sqrt[4]{{{{\left( {3 + 2\sqrt 2 } \right)}^2}}} - \sqrt 2 \\
= \sqrt {3 + 2\sqrt 2 } - \sqrt 2 \\
= \sqrt {2 + 2\sqrt 2 .1 + 1} - \sqrt 2 \\
= \sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} - \sqrt 2 \\
= \sqrt 2 + 1 - \sqrt 2 = 1\\
c)\sqrt[4]{{36 - 2.6.2\sqrt 5 + 20}}\\
= \sqrt[4]{{{{\left( {6 - 2\sqrt 5 } \right)}^2}}}\\
= \sqrt {6 - 2\sqrt 5 } \\
= \sqrt {5 - 2\sqrt 5 .1 + 1} \\
= \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\
= \sqrt 5 - 1\\
d)1 + \sqrt[4]{{16 - 2.4.2\sqrt 3 + 12}}\\
= 1 + \sqrt[4]{{{{\left( {4 - 2\sqrt 3 } \right)}^2}}}\\
= 1 + \sqrt {4 - 2\sqrt 3 } \\
= 1 + \sqrt {3 - 2\sqrt 3 .1 + 1} \\
= 1 + \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \\
= 1 + \sqrt 3 - 1 = \sqrt 3
\end{array}\)
