Đáp án:
2) \(\dfrac{{\sqrt 5 + \sqrt 2 }}{3}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\sqrt {5 - \sqrt {13 + \sqrt {48} } } \\
= \sqrt {5 - \sqrt {13 + 4\sqrt 3 } } \\
= \sqrt {5 - \sqrt {12 + 2.2\sqrt 3 .1 + 1} } \\
= \sqrt {5 - \sqrt {{{\left( {2\sqrt 3 + 1} \right)}^2}} } \\
= \sqrt {5 - \left( {2\sqrt 3 + 1} \right)} \\
= \sqrt {4 - 2\sqrt 3 } \\
= \sqrt {3 - 2.\sqrt 3 .1 + 1} \\
= \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \\
2)\dfrac{{\sqrt {\sqrt 5 + \sqrt 2 } }}{{\sqrt {3\sqrt 5 - 3\sqrt 2 } }}\\
= \dfrac{{\sqrt {\sqrt 5 + \sqrt 2 } }}{{\sqrt {3\left( {\sqrt 5 - \sqrt 2 } \right)} }}\\
= \sqrt {\dfrac{{{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2}}}{{3.\left( {5 - 2} \right)}}} = \dfrac{{\sqrt 5 + \sqrt 2 }}{{\sqrt {3.3} }}\\
= \dfrac{{\sqrt 5 + \sqrt 2 }}{3}\\
3)\dfrac{{\sqrt {8 - \sqrt {15} } }}{{\sqrt {30} - \sqrt 2 }} = \dfrac{{\sqrt {16 - 2\sqrt {15} } }}{{2\sqrt {15} - 2}}\\
= \dfrac{{\sqrt {15 - 2.\sqrt {15} .1 + 1} }}{{2\left( {\sqrt {15} - 1} \right)}}\\
= \dfrac{{\sqrt {{{\left( {\sqrt {15} - 1} \right)}^2}} }}{{2\left( {\sqrt {15} - 1} \right)}}\\
= \dfrac{{\sqrt {15} - 1}}{{2\left( {\sqrt {15} - 1} \right)}} = \dfrac{1}{2}
\end{array}\)
