\(\begin{array}{l}a)\sqrt {0,49}  + \sqrt {0,64}  = 0,7 + 0,8 = 1,5;\\b)\sqrt {0,36}  - \sqrt {0,81}  = 0,6 - 0,9 =  - 0,3;\\c)8.\sqrt 9  - \sqrt {64}  = 8.3 - 8 = 24 - 8 = 16;\\d)0,1.\sqrt {400}  + 0,2.\sqrt {1600}  = 0,1.20 + 0,2.40 = 2 + 8 = 10\end{array}\)

\(\sqrt{1600^2-400^2}=1549,193338\)

\(\sqrt{1600^2-400^2}=400\sqrt{15}\)

\(\sqrt{1200^2-300^2}=2^2\cdot3\cdot5^2\sqrt{15}\)

\(\sqrt{1200^2-300^2}=1161,895004\)

a) \(\sqrt{4,9.1350.0,6}=\frac{7\sqrt{10}}{10}.15\sqrt{6}.\frac{\sqrt{15}}{5}=63\)

b) \(\sqrt{12,5}.\sqrt{0,2}.\sqrt{0,1}=\frac{5\sqrt{2}}{2}.\frac{\sqrt{5}}{5}.\frac{\sqrt{10}}{10}=\frac{1}{2}\)

c) \(\sqrt{\frac{484}{169}}=\frac{22}{13}\)

d) \(\sqrt{\frac{2}{288}}=\sqrt{\frac{1}{144}}=\frac{1}{12}\)

e) \(\frac{\sqrt{2^5}}{\sqrt{2^3}}=\sqrt{2^2}=2\)

\(\begin{array}{l}a)\sqrt {1600}  = 40;\\b)\sqrt {0,16}  = 0,4;\\c)\sqrt {2\frac{1}{4}}  = \sqrt {\frac{9}{4}}  = \frac{3}{2}\end{array}\)

\(\text{a)}\sqrt{1600}=40\)

\(\text{b)}\sqrt{0,16}=0,4\)

\(\text{c)}\sqrt{2\dfrac{1}{4}}=\sqrt{\dfrac{9}{4}}=\dfrac{3}{2}\)

\(\begin{array}{l}a)2.\sqrt 6 .( - \sqrt 6 )\\ =  - 2.\sqrt 6 .\sqrt 6 \\ =  - 2.{(\sqrt 6 )^2}\\ =  - 2.6\\ =  - 12\\b)\sqrt {1,44}  - 2.{(\sqrt {0,6} )^2}\\ = 1,2 - 2.0,6\\ = 1,2 - 1,2\\ = 0\\c)0,1.{(\sqrt 7 )^2} + \sqrt {1,69} \\ = 0,1.7 + 1,3 \\= 0,7 + 1,3 \\= 2\\d)( - 0,1).{(\sqrt {120} )^2} - \frac{1}{4}.{(\sqrt {20} )^2} \\= ( - 0,1).120 - \frac{1}{4}.20\\ =  - 12 - 5\\ =  - (12 + 5)\\ =  - 17\end{array}\)

a: \(=-2\sqrt{6}\cdot\sqrt{6}=-2\cdot\sqrt{6\cdot6}=-2\cdot6=-12\)

b: \(=1.2-2\cdot0.6=1.2-1.2=0\)

c: \(=0.1\cdot7+1.3=0.7+1.3=2\)

d: \(=-0.1\cdot120-\dfrac{1}{4}\cdot20=-12-5=-17\)

\(\sqrt{10}A=\sqrt{10}\left(\sqrt{0,1}+\sqrt{0,9}+\sqrt{6,4}+\sqrt{0,4}+\sqrt{44,1}\right)\)

\(=\sqrt{1}+\sqrt{9}+\sqrt{64}+\sqrt{4}+\sqrt{441}\)

\(=1+3+8+2+21=35\)

\(\Rightarrow A=\frac{35}{\sqrt{10}}\)

B1:

1. \(\sqrt{12.5}\cdot\sqrt{0.2}\cdot\sqrt{0.1}\) \(=\sqrt{12.5\cdot0.2\cdot0.1}\) \(=\sqrt{0.25}=0.5\)

2.\(\sqrt{48.4}\cdot\sqrt{5}\cdot\sqrt{0.5}\) = \(\sqrt{48.4\cdot5\cdot0.5}\) =\(\sqrt{121}=11\)

B2:

a, \(\left(\sqrt{7}+\sqrt{3}\right)^2=7+2\cdot\sqrt{7}\cdot\sqrt{3}+3=7+2\cdot\sqrt{21}+3\)\(=10+2\sqrt{21}\)

b,\(\left(\sqrt{11}-\sqrt{5}\right)^2=11-2\sqrt{55}+5=16-2\sqrt{55}\)

c,\(\left(\sqrt{x}+\sqrt{y}\right) ^2=x+2\sqrt{xy}+y\)

d.\(\left(\sqrt{13}+\sqrt{7}\right)^2=13+2\sqrt{7}+7=20+2\sqrt{7}\)

e,\(\left(\sqrt{a}-\sqrt{b}\right)^2=a-2\sqrt{ab}+b\)

f,\(\left(\sqrt{3}-1\right)^2=3-2\sqrt{3}+1=4-2\sqrt{3}\)