Đáp án:
$\begin{array}{l}
11)\\
\sqrt 3 + \sqrt {15} = \sqrt 3 \left( {1 + \sqrt 5 } \right)\\
12)\\
\sqrt {21} + \sqrt 7 = \sqrt 7 \left( {\sqrt 3 + 1} \right)\\
13)\\
\sqrt {xy} + 2\sqrt x - 3\sqrt y - \sqrt 6 \\
= \sqrt x \left( {\sqrt y + 2} \right) - 3\left( {\sqrt y + 2} \right)\\
= \left( {\sqrt y + 2} \right)\left( {\sqrt x - 3} \right)\\
14)\\
x + 2\sqrt {xy} + y = {\left( {\sqrt x + \sqrt y } \right)^2}\\
15)\\
x + 2\sqrt x - 4y - 4\sqrt y \\
= x - 4y + 2\left( {\sqrt x - 2\sqrt y } \right)\\
= \left( {\sqrt x - 2\sqrt y } \right)\left( {\sqrt x + 2\sqrt y + 2} \right)\\
16)\\
4 - m = \left( {2 + \sqrt m } \right)\left( {2 - \sqrt m } \right)\\
17)\\
3 - \sqrt 6 + \sqrt 3 = \sqrt 3 \left( {\sqrt 3 - \sqrt 2 + 1} \right)\\
18)\\
x - 2\sqrt x - 3 = \left( {\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)\\
19)\\
x - 4\sqrt {xy} + 4y - 9\\
= {\left( {\sqrt x - 2\sqrt y } \right)^2} - 9\\
= \left( {\sqrt x - 2\sqrt y + 2} \right)\left( {\sqrt x + 2\sqrt y - 2} \right)\\
20)\\
5x - 5\sqrt {xy} - 2\sqrt x + 2\sqrt y \\
= \left( {\sqrt x - \sqrt y } \right)\left( {5\sqrt x - 2} \right)\\
21){x^2} + 8\sqrt x = \sqrt x \left( {x\sqrt x + 8} \right)\\
= \sqrt x \left( {\sqrt x + 2} \right)\left( {x - 2\sqrt x + 4} \right)\\
22)15 - 2 = 13\\
24)xy + y\sqrt x + \sqrt x + 1\\
= \left( {\sqrt x + 1} \right)\left( {y\sqrt x + 1} \right)\\
25)\\
6 - x - \sqrt x \\
= - \left( {x + \sqrt x - 6} \right)\\
= - \left( {\sqrt x - 2} \right)\left( {\sqrt x + 3} \right)\\
= \left( {2 - \sqrt x } \right)\left( {\sqrt x + 3} \right)\\
26)\\
19 + 6\sqrt 2 = {\left( {3\sqrt 2 + 1} \right)^2}\\
27)\\
15 + 10\sqrt 2 = 5\left( {3 + 2\sqrt 2 } \right)\\
28)\\
57 - 8\sqrt {41} = {\left( {\sqrt {41} - 4} \right)^2}\\
29)\\
41 + 6\sqrt {20} = \\
30)38 + 12\sqrt 2 \\
= 36 + 2.6.\sqrt 2 + 2\\
= {\left( {6 + \sqrt 2 } \right)^2}
\end{array}$
