Đáp án:
\(\sqrt 2 \)
Giải thích các bước giải:
\(\begin{array}{l}
\,\,\,\,\left( {2 - \sqrt 3 } \right)\sqrt {26 + 15\sqrt 3 } - \left( {2 + \sqrt 3 } \right)\sqrt {26 - 15\sqrt 3 } \\
= \dfrac{1}{{\sqrt 2 }}\left( {2 - \sqrt 3 } \right)\sqrt {52 + 30\sqrt 3 } - \dfrac{1}{{\sqrt 2 }}\left( {2 + \sqrt 3 } \right)\sqrt {52 - 15\sqrt 3 } \\
= \dfrac{1}{{\sqrt 2 }}\left[ {\left( {2 - \sqrt 3 } \right)\sqrt {{{\left( {3\sqrt 3 + 5} \right)}^2}} - \left( {2 + \sqrt 3 } \right)\sqrt {{{\left( {3\sqrt 3 - 5} \right)}^2}} } \right]\\
= \dfrac{1}{{\sqrt 2 }}\left[ {\left( {2 - \sqrt 3 } \right)\left( {3\sqrt 3 + 5} \right) - \left( {2 + \sqrt 3 } \right)\left( {3\sqrt 3 - 5} \right)} \right]\\
= \dfrac{1}{{\sqrt 2 }}\left( {1 + \sqrt 3 + 1 - \sqrt 3 } \right)\\
= \dfrac{1}{{\sqrt 2 }}.2\\
= \sqrt 2
\end{array}\)
