Đáp án:
$\begin{array}{l}
a)2\sqrt {27} = \sqrt {4.27} = \sqrt {108} < \sqrt {147} \\
\Rightarrow 2\sqrt {27} < \sqrt {147} \\
b) - 3\sqrt 5 = - \sqrt {45} \\
- 5\sqrt 3 = - \sqrt {75} \\
Do:\sqrt {45} < \sqrt {75} \\
\Rightarrow - \sqrt {45} > - \sqrt {75} \\
\Rightarrow - 3\sqrt 5 > - 5\sqrt 3 \\
d)2\sqrt {15} = \sqrt {60} > \sqrt {59} \\
e)2\sqrt 2 - 1\\
= \sqrt 8 - 1\\
2 = 3 - 1 = \sqrt 9 - 1\\
\Rightarrow 2\sqrt 2 - 1 < 2\\
g)\dfrac{{\sqrt 3 }}{2} < \dfrac{{\sqrt 4 }}{2} = 1\\
h) - \dfrac{{\sqrt {10} }}{2}\\
- 2\sqrt 5 = - \dfrac{{4\sqrt 5 }}{2} = - \dfrac{{\sqrt {80} }}{2}\\
\Rightarrow - \dfrac{{\sqrt {10} }}{2} > - 2\sqrt 5 \\
j)2\sqrt 5 - 5\sqrt 2 \\
= \sqrt {20} - \sqrt {50} < 0 < 1\\
k)\dfrac{{\sqrt 8 }}{3} = \dfrac{{4\sqrt 8 }}{{12}} = \dfrac{{\sqrt {128} }}{{12}}\\
\dfrac{3}{4} = \dfrac{9}{{12}} = \dfrac{{\sqrt {81} }}{{12}}\\
\Rightarrow \dfrac{{\sqrt 8 }}{3} < \dfrac{3}{4}\\
m) - 2\sqrt 6 = - \sqrt {24} < - \sqrt {23} \\
n)2\sqrt 6 - 2 = \sqrt {24} - 2\\
3 = 5 - 2 = \sqrt {25} - 2\\
\Rightarrow 2\sqrt 6 - 2 < 3\\
q)\sqrt 9 = 3\\
\sqrt {25} - \sqrt {16} = 5 - 4 = 1\\
\Rightarrow \sqrt 9 > \sqrt {25} - \sqrt {16} \\
r)\sqrt {111} - 7\\
4 = 11 - 7 = \sqrt {121} - 7\\
\Rightarrow \sqrt {111} - 7 < 4
\end{array}$
