\(=3\sqrt{2}-3\sqrt{2}+2\sqrt{2}+6\sqrt{2}=8\sqrt{2}\)

a) \(\sqrt{200}-\sqrt{32}+\sqrt{72}\)

\(=\sqrt{10^2\cdot2}-\sqrt{4^2\cdot2}+\sqrt{6^2\cdot2}\)

\(=10\sqrt{2}-4\sqrt{2}+6\sqrt{2}\)

\(=\left(10-4+6\right)\sqrt{2}\)

\(=12\sqrt{2}\)

b) \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)

\(=4\cdot2\sqrt{5}-3\cdot5\sqrt{5}+5\cdot3\sqrt{5}-3\sqrt{5}\)

\(=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}\)

\(=\left(8-15+15-3\right)\sqrt{5}\)

\(=5\sqrt{5}\)

c) \(\left(2\sqrt{8}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\sqrt{20}-2\sqrt{2}\right)\)

\(=\left(2\cdot2\sqrt{2}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\cdot2\sqrt{5}-2\sqrt{2}\right)\)

\(=\left(3\sqrt{5}-3\sqrt{2}\right)\left(72-10\sqrt{5}-2\sqrt{2}\right)\)

\(\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{72}\)

\(=3-\sqrt{2}+6\sqrt{2}\)

\(=5\sqrt{2}+3\)

= \(3-\sqrt{2}+6\sqrt{2}\)

= \(5\sqrt{2}+3\)

Tính:

a,  . +  : 

 7 . 12 + 16 : 8 

   = 84 + 2

    = 86

b, 72 :  - 

 2.6.3-15

= -13

\(-\dfrac{6\sqrt{2}-\sqrt{\left(9-8\sqrt{2}\right)\cdot2}}{2}\)

\(\sqrt{2.36}+\sqrt{2.\dfrac{9}{4}}-\sqrt{2.16}-\sqrt{2.81}=6\sqrt{2}+\dfrac{3}{2}\sqrt{2}-4\sqrt{2}-9\sqrt{2}=\dfrac{-11}{2}\sqrt{2}\)

\(\sqrt{4\dfrac{1}{2}}+\sqrt{32}-\sqrt{72}+\sqrt{162}\\ =\sqrt{\dfrac{4\cdot2+1}{2}}+\sqrt{4^2\cdot2}-\sqrt{6^2\cdot2}+\sqrt{9^2\cdot2}\\ =\sqrt{\dfrac{9}{2}}+4\sqrt{2}-6\sqrt{2}+9\sqrt{2}\\ =\dfrac{3}{\sqrt{2}}+7\sqrt{2}\\ =\dfrac{3}{\sqrt{2}}+\dfrac{7\sqrt{2}\cdot\sqrt{2}}{\sqrt{2}}\\ =\dfrac{17}{\sqrt{2}}\)

\(=\sqrt{\dfrac{9}{2}}+4\sqrt{2}-6\sqrt{2}+9\sqrt{2}\)

\(=\dfrac{3}{2}\sqrt{2}+7\sqrt{2}=\dfrac{17}{2}\sqrt{2}\)

\(\sqrt{4\dfrac{1}{2}}+\sqrt{32}-\sqrt{72}+\sqrt{162}\)

\(=\sqrt{\dfrac{9}{2}}+\sqrt{4^2.2}-\sqrt{6^2.2}+\sqrt{9^2.2}\)

\(=\dfrac{3}{\sqrt{2}}+4\sqrt{2}-6\sqrt{2}+9\sqrt{2}\)

\(=\dfrac{3\sqrt{2}}{2}+7\sqrt{2}=\dfrac{3\sqrt{2}+14\sqrt{2}}{2}=\dfrac{17\sqrt{2}}{2}\)

6: Ta có: \(\left(3\sqrt{2}-\sqrt{3}\right)\left(3\sqrt{2}+\sqrt{3}\right)\)

=18-3

=15

7: Ta có: \(\sqrt{72}+\sqrt{4\dfrac{1}{2}}-\sqrt{32}-\sqrt{162}\)

\(=6\sqrt{2}+\dfrac{3}{2}\sqrt{2}-4\sqrt{2}-9\sqrt{2}\)

\(=-\dfrac{11}{2}\sqrt{2}\)

\sqrt{72}\+ \sqrt{4+1/2}\ - \sqrt{32}\ -\sqrt{162}\

\(B=\left(\dfrac{3-2\sqrt{2}-3-2\sqrt{2}}{-1}\right):6\sqrt{2}=\dfrac{4\sqrt{2}}{6\sqrt{2}}=\dfrac{2}{3}\)

\(\left(\frac{1-\sqrt{2}}{1+\sqrt{2}}-\frac{1+\sqrt{2}}{1-\sqrt{2}}\right):\sqrt{72}\)

\(\left[\frac{\left(1-\sqrt{2}\right)^2-\left(1+\sqrt{2}\right)^2}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}\right]:\sqrt{72}\)

\(=\frac{1-2\sqrt{2}+2-1-2\sqrt{2}-2}{1-2}\cdot\frac{1}{\sqrt{72}}\)

\(=\frac{-2\sqrt{2}-2\sqrt{2}}{-1}\cdot\frac{1}{\sqrt{72}}\)

\(=4\sqrt{2}\cdot\frac{1}{2\sqrt{18}}=\frac{2}{\sqrt{9}}=\frac{2}{3}\)