Đáp án:
\(\begin{array}{l}
h)2\sqrt 2 \\
j)11 + 4\sqrt 3 \\
i)4\sqrt 3 - 7\sqrt 2 \\
k)15 - 14\sqrt 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
h){\left( {1 + \sqrt 2 } \right)^2} - {\left( {\sqrt 3 } \right)^2}\\
= \left( {3 + 2\sqrt 2 } \right) - 3\\
= 2\sqrt 2 \\
j){\left( {1 + 2\sqrt 3 } \right)^2} - {\left( {\sqrt 2 } \right)^2}\\
= \left( {1 + 4\sqrt 3 + 12} \right) - 2\\
= 11 + 4\sqrt 3 \\
i)\sqrt 3 \left( {2 - 2\sqrt 6 + 3} \right) - \sqrt 3 - \sqrt 2 \\
= 2\sqrt 3 - 6\sqrt 2 + 3\sqrt 3 - \sqrt 3 - \sqrt 2 \\
= 4\sqrt 3 - 7\sqrt 2 \\
k)\left( {1 - 2\sqrt 3 + 3} \right)\left( {1 + 4\sqrt 3 + 12} \right)\\
= \left( {3 - 2\sqrt 3 } \right)\left( {13 + 4\sqrt 3 } \right)\\
= 39 + 12\sqrt 3 - 26\sqrt 3 - 8.3\\
= 15 - 14\sqrt 3
\end{array}\)
