Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\sqrt {{{\left( {2 - \sqrt 5 } \right)}^2}} + \sqrt {20} \\
= \left| {2 - \sqrt 5 } \right| + \sqrt {{2^2}.5} \\
= \left( {\sqrt 5 - 2} \right) + 2.\sqrt 5 \\
= 3\sqrt 5 - 2\\
b,\\
\sqrt {75} + \sqrt {48} - \sqrt {300} \\
= \sqrt {25.3} + \sqrt {16.3} - \sqrt {100.3} \\
= \sqrt {{5^2}.3} + \sqrt {{4^2}.3} - \sqrt {{{10}^2}.3} \\
= 5\sqrt 3 + 4\sqrt 3 - 10\sqrt 3 \\
= - \sqrt 3 \\
c,\\
\dfrac{4}{{\sqrt 5 - 2}} - \dfrac{4}{{\sqrt 5 + 2}}\\
= \dfrac{{4.\left( {\sqrt 5 + 2} \right) - 4.\left( {\sqrt 5 - 2} \right)}}{{\left( {\sqrt 5 - 2} \right)\left( {\sqrt 5 + 2} \right)}}\\
= \dfrac{{4\sqrt 5 + 8 - 4\sqrt 5 + 8}}{{{{\sqrt 5 }^2} - {2^2}}}\\
= \dfrac{{16}}{1}\\
= 16\\
d,\\
A = \sqrt {{{\left( {2a + 5} \right)}^2}} - \left( {2a - 7} \right)\\
= \left| {2a + 5} \right| - 2a + 7\\
TH1:\,\,\,a \ge - \dfrac{5}{2} \Rightarrow 2a + 5 \ge 0 \Rightarrow \left| {2a + 5} \right| = 2a + 5\\
\Rightarrow A = 2a + 5 - 2a + 7 = 12\\
TH2:\,\,\,a < - \dfrac{5}{2} \Rightarrow 2a + 5 < 0 \Rightarrow \left| {2a + 5} \right| = - \left( {2a + 5} \right)\\
\Rightarrow A = - \left( {2a + 5} \right) - 2a + 7 = - 4a + 2
\end{array}\)
