Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
5\sqrt {\dfrac{1}{5}} + \dfrac{1}{2}\sqrt {20} + \sqrt 5 \\
= \sqrt {{5^2}.\dfrac{1}{5}} + \dfrac{1}{2}.\sqrt {{2^2}.5} + \sqrt 5 \\
= \sqrt 5 + \dfrac{1}{2}.2\sqrt 5 + \sqrt 5 \\
= \sqrt 5 + \sqrt 5 + \sqrt 5 = 3\sqrt 5 \\
b,\\
\sqrt {\dfrac{1}{2}} + \sqrt {4,5} + \sqrt {12,5} \\
= \dfrac{1}{{\sqrt 2 }} + \sqrt {\dfrac{9}{2}} + \sqrt {\dfrac{{25}}{2}} \\
= \dfrac{1}{{\sqrt 2 }} + \dfrac{3}{{\sqrt 2 }} + \dfrac{5}{{\sqrt 2 }}\\
= \dfrac{9}{{\sqrt 2 }} = \dfrac{{9\sqrt 2 }}{2}\\
c,\\
\sqrt {20} - \sqrt {45} + 3\sqrt {18} + \sqrt {72} \\
= \sqrt {{2^2}.5} - \sqrt {{3^2}.5} + 3.\sqrt {{3^2}.2} + \sqrt {{6^2}.2} \\
= 2\sqrt 5 - 3\sqrt 5 + 3.3\sqrt 2 + 6\sqrt 2 \\
= - \sqrt 5 + 15\sqrt 2 \\
d,\\
0,1.\sqrt {200} + 2.\sqrt {0,08} + 0,4.\sqrt {50} \\
= 0,1.\sqrt {{{10}^2}.2} + 2.\sqrt {0,{2^2}.2} + 0,4.\sqrt {{5^2}.2} \\
= 0,1.10.\sqrt 2 + 2.0,2.\sqrt 2 + 0,4.5.\sqrt 2 \\
= 1.\sqrt 2 + 0,4\sqrt 2 + 2.\sqrt 2 \\
= 3,4.\sqrt 2 \\
2,\\
a,\\
5\sqrt a - 4b\sqrt {25{a^3}} + 5a.\sqrt {16a{b^2}} - 2.\sqrt {9a} \\
= 5\sqrt a - 4b.\sqrt {{{\left( {5a} \right)}^2}.a} + 5a.\sqrt {{{\left( {4b} \right)}^2}.a} - 2.\sqrt {{3^2}.a} \\
= 5\sqrt a - 4b.5a.\sqrt a + 5a.4b.\sqrt a - 2.3.\sqrt a \\
= 5\sqrt a - 20ab\sqrt a + 20\sqrt a - 6\sqrt a \\
= - \sqrt a \\
b,\\
5a\sqrt {64a{b^3}} - \sqrt 3 .\sqrt {12{a^3}{b^3}} + 2ab\sqrt {9ab} - 5b\sqrt {81{a^3}b} \\
= 5a.\sqrt {{{\left( {8b} \right)}^2}.ab} - \sqrt 3 .\sqrt {{{\left( {2\sqrt 3 ab} \right)}^2}.ab} + 2ab.\sqrt {{3^2}.ab} - 5b\sqrt {{{\left( {9a} \right)}^2}.ab} \\
= 5a.8b.\sqrt {ab} - \sqrt 3 .2\sqrt 3 ab.\sqrt {ab} + 2ab.3.\sqrt {ab} - 5b.9a.\sqrt {ab} \\
= 40ab\sqrt {ab} - 6ab\sqrt {ab} + 6ab\sqrt {ab} - 45ab\sqrt {ab} \\
= - 5ab\sqrt {ab}
\end{array}\)
