Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\sqrt {11 - 2\sqrt {10} } = \sqrt {10 - 2.\sqrt {10} .1 + 1} = \sqrt {{{\left( {\sqrt {10} - 1} \right)}^2}} = \sqrt {10} - 1\\
b,\\
\sqrt {9 - 2\sqrt {14} } = \sqrt {7 - 2.\sqrt 7 .\sqrt 2 + 2} = \sqrt {{{\left( {\sqrt 7 - \sqrt 2 } \right)}^2}} = \sqrt 7 - \sqrt 2 \\
c,\\
\sqrt {4 + 2\sqrt 3 } - \sqrt {4 - 2\sqrt 3 } \\
= \sqrt {3 + 2\sqrt 3 .1 + 1} - \sqrt {3 - 2.\sqrt 3 .1 + 1} \\
= \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \\
= \left( {\sqrt 3 + 1} \right) - \left( {\sqrt 3 - 1} \right)\\
= 2\\
d,\\
\sqrt {4 - \sqrt 7 } - \sqrt {4 - \sqrt 7 } = 0\\
e,\\
\sqrt {5\sqrt 3 + 5\sqrt {48 - 10\sqrt {7 + 4\sqrt 3 } } } \\
= \sqrt {5\sqrt 3 + 5\sqrt {48 - 10\sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} } } \\
= \sqrt {5\sqrt 3 + 5\sqrt {48 - 10\left( {2 + \sqrt 3 } \right)} } \\
= \sqrt {5\sqrt 3 + 5\sqrt {28 - 10\sqrt 3 } } \\
= \sqrt {5\sqrt 3 + 5\sqrt {{{\left( {5 - \sqrt 3 } \right)}^2}} } \\
= \sqrt {5\sqrt 3 + 5.\left( {5 - \sqrt 3 } \right)} \\
= \sqrt {25} \\
= 5
\end{array}\)
