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a) ( 75 - 3 2 - 12 )( 3 + 2 )
=(5 3 - 3 2 - 2 3 )( 3 + 2 )
=3( 3 - 2 )( 3 + 2 ) = 3
a) \(\left(2\sqrt{2}-3\right)^2\)
\(=\left(2\sqrt{2}\right)^2-2\cdot2\sqrt{2}\cdot3+3^2\)
\(=4\cdot2-12\sqrt{2}+9\)
\(=17-12\sqrt{2}\)
b) \(\sqrt{\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{2}\right)^2}\)
\(=\left|\dfrac{1}{\sqrt{2}}-\dfrac{1}{2}\right|\)
\(=\dfrac{1}{\sqrt{2}}-\dfrac{1}{2}\)
\(=\dfrac{\sqrt{2}}{2}-\dfrac{1}{2}\)
\(=\dfrac{\sqrt{2}-1}{2}\)
c) \(\sqrt{\left(0,1-\sqrt{0,1}\right)^2}\)
\(=\left|0,1-\sqrt{0,1}\right|\)
\(=0,1-\sqrt{0,1}\)
a: \(=\sqrt{3}-\sqrt{2}+3\sqrt{2}=2\sqrt{2}+\sqrt{3}\)
\(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}+1}-\left(2+\sqrt{3}\right)\\ =\dfrac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-2-\sqrt{3}\\ =\sqrt{3}+2+\sqrt{2}-2-\sqrt{3}\\ =\sqrt{2}\)
\(a.\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}=\left|\sqrt{2}-\sqrt{3}\right|+3\sqrt{2}=\sqrt{3}-\sqrt{2}+3\sqrt{2}\left(\sqrt{3}>\sqrt{2}\right)=\sqrt{3}+2\sqrt{2}\)\(b.3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}=3\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}=-6\sqrt{2}\)
b) 3 - 2 2 2 + 3 + 2 2 2
= 3 - 2 2 + 3 + 2 2
= 3 - 2 2 + 3 + 2 2
= 6