Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
3,\\
a,\\
\sqrt {2x + 14}  = 15\,\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge  - 7} \right)\\
 \Leftrightarrow {\sqrt {2x + 14} ^2} = {15^2}\\
 \Leftrightarrow 2x + 14 = 225\\
 \Leftrightarrow 2x = 211\\
 \Leftrightarrow x = \dfrac{{211}}{2}\\
b,\\
\sqrt {3 - 2x}  = 7\,\,\,\,\,\,\,\,\,\,\,\left( {x \le \dfrac{3}{2}} \right)\\
 \Leftrightarrow {\sqrt {3 - 2x} ^2} = {7^2}\\
 \Leftrightarrow 3 - 2x = 49\\
 \Leftrightarrow 2x =  - 46\\
 \Leftrightarrow x =  - 23\\
c,\,\,\,\,\,2\sqrt {4x + 1}  - 8 = 2\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge  - \dfrac{1}{4}} \right)\\
 \Leftrightarrow 2\sqrt {4x + 1}  = 10\\
 \Leftrightarrow \sqrt {4x + 1}  = 5\\
 \Leftrightarrow 4x + 1 = 25\\
 \Leftrightarrow 4x = 24\\
 \Leftrightarrow x = 6\\
d,\,\,\,\,\,\,7 - 2\sqrt {3x - 1}  =  - 5\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge \dfrac{1}{3}} \right)\\
 \Leftrightarrow 2\sqrt {3x - 1}  = 12\\
 \Leftrightarrow \sqrt {3x - 1}  = 6\\
 \Leftrightarrow 3x - 1 = 36\\
 \Leftrightarrow 3x = 37\\
 \Leftrightarrow x = \dfrac{{37}}{3}\\
e,\,\,\,\,\,\,14 - 3\sqrt {x + 5}  =  - 7\,\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge  - 5} \right)\\
 \Leftrightarrow 3\sqrt {x + 5}  = 21\\
 \Leftrightarrow \sqrt {x + 5}  = 7\\
 \Leftrightarrow x + 5 = 49\\
 \Leftrightarrow x = 42\\
4,\\
a,\,\,\,\,\sqrt {4x + 4}  - 2\sqrt {9x + 9}  + 3\sqrt {16x + 16}  = 5\,\,\,\,\,\,\,\,\,\,\left( {x \ge  - 1} \right)\\
 \Leftrightarrow \sqrt {4.\left( {x + 1} \right)}  - 2.\sqrt {9\left( {x + 1} \right)}  + 3.\sqrt {16\left( {x + 1} \right)}  = 5\\
 \Leftrightarrow 2\sqrt {x + 1}  - 2.3\sqrt {x + 1}  + 3.4\sqrt {x + 1}  = 5\\
 \Leftrightarrow 2\sqrt {x + 1}  - 6\sqrt {x + 1}  + 12\sqrt {x + 1}  = 5\\
 \Leftrightarrow 8\sqrt {x + 1}  = 5\\
 \Leftrightarrow \sqrt {x + 1}  = \dfrac{5}{8}\\
 \Leftrightarrow x + 1 = \dfrac{{25}}{{64}}\\
 \Leftrightarrow x =  - \dfrac{{39}}{{64}}\\
b,\,\,\,\,\sqrt {25x - 25}  - 7\sqrt {36x - 36}  + 37 = 0\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge 1} \right)\\
 \Leftrightarrow \sqrt {25\left( {x - 1} \right)}  - 7.\sqrt {36\left( {x - 1} \right)}  + 37 = 0\\
 \Leftrightarrow 5\sqrt {x - 1}  - 7.6\sqrt {x - 1}  + 37 = 0\\
 \Leftrightarrow 5\sqrt {x - 1}  - 42\sqrt {x - 1}  + 37 = 0\\
 \Leftrightarrow  - 37\sqrt {x - 1}  + 37 = 0\\
 \Leftrightarrow \sqrt {x - 1}  = 1\\
 \Leftrightarrow x - 1 = 1\\
 \Leftrightarrow x = 2\\
c,\,\,\,\,\,\,\,\sqrt 2 x - \sqrt {18}  = 0\\
 \Leftrightarrow \sqrt 2 x = \sqrt {18} \\
 \Leftrightarrow x = \sqrt 9 \\
 \Leftrightarrow x = 3\\
d,\,\,\,\,\,\sqrt 3  - x - \sqrt {27}  = 0\\
 \Leftrightarrow \sqrt 3  - x - 3\sqrt 3  = 0\\
 \Leftrightarrow x =  - 2\sqrt 3 \\
e,\\
\left( {\sqrt 2  + 1} \right)x = 3 + 2\sqrt 2 \\
 \Leftrightarrow \left( {\sqrt 2  + 1} \right)x = 2 + 2.\sqrt 2 .1 + 1\\
 \Leftrightarrow \left( {\sqrt 2  + 1} \right)x = {\left( {\sqrt 2  + 1} \right)^2}\\
 \Leftrightarrow x = \sqrt 2  + 1
\end{array}\)