Đáp án:
\[A = 2\sqrt 2 \]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = \left( {\sqrt 5 + 3} \right).\sqrt {7 - 3\sqrt 5 } \\
= \dfrac{1}{{\sqrt 2 }}.\left( {\sqrt 5 + 3} \right).\sqrt 2 .\sqrt {7 - 3\sqrt 5 } \\
= \dfrac{1}{{\sqrt 2 }}.\left( {\sqrt 5 + 3} \right).\sqrt {2.\left( {7 - 3\sqrt 5 } \right)} \\
= \dfrac{1}{{\sqrt 2 }}.\left( {\sqrt 5 + 3} \right).\sqrt {14 - 6\sqrt 5 } \\
= \dfrac{1}{{\sqrt 2 }}.\left( {\sqrt 5 + 3} \right).\sqrt {{3^2} - 2.3.\sqrt 5 + 5} \\
= \dfrac{1}{{\sqrt 2 }}.\left( {\sqrt 5 + 3} \right).\sqrt {{{\left( {\sqrt 5 - 3} \right)}^2}} \\
= \dfrac{1}{{\sqrt 2 }}.\left( {3 + \sqrt 5 } \right).\left( {3 - \sqrt 5 } \right)\\
= \dfrac{1}{{\sqrt 2 }}.\left( {{3^2} - {{\sqrt 5 }^2}} \right)\\
= \dfrac{1}{{\sqrt 2 }}.4\\
= 2\sqrt 2
\end{array}\)
