b)
\(\sqrt{\left(4-2\sqrt{3}\right)\left(13+4\sqrt{3}\right)}\)
\(=\sqrt{\left(3-2\sqrt{3}+1\right)\left(12+4\sqrt{3}+1\right)}\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2\cdot\left(\sqrt{12}+1\right)^2}\)
\(=\left|\sqrt{3}-1\right|\cdot\left|\sqrt{12}+1\right|\)
\(=\left(\sqrt{3}-1\right)\left(2\sqrt{3}+1\right)\) ( vì \(\sqrt{3}-1>0;2\sqrt{3}+1>0\) )
\(=6+\sqrt{3}-2\sqrt{3}-1\)
\(=5-\sqrt{3}\)
c)
\(\left(\sqrt{3}-2\right)\left(\sqrt{6}+\sqrt{2}\right)\sqrt{\sqrt{3}+2}\)
\(=\left(\sqrt{18}+\sqrt{6}-2\sqrt{6}-2\sqrt{2}\right)\cdot\dfrac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\)
\(=\left(\sqrt{18}-\sqrt{6}-2\sqrt{2}\right)\cdot\dfrac{\sqrt{3+2\sqrt{3}+1}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{2}\left(\sqrt{9}-\sqrt{3}-2\right)\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}\)
\(=\left(3-\sqrt{3}-2\right)\left|\sqrt{3}+1\right|\)
\(=\left(1-\sqrt{3}\right)\left(\sqrt{3}+1\right)\) ( vì \(\sqrt{3}+1>0\) )
`=1-3`
`=-2`
a)
\(\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{5-2\sqrt{5}+1}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{\left(\sqrt{5}-1\right)^2}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\left|\sqrt{5}-1\right|}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{4+\sqrt{5}-1}\) (vì \(\sqrt{5}-1>0\) )
\(=\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3+\sqrt{5}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\cdot\dfrac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\cdot\dfrac{\sqrt{5+2\sqrt{5}+1}}{\sqrt{2}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\cdot\dfrac{\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}\)
\(=\left(\sqrt{10}-\sqrt{2}\right)\cdot\dfrac{\left|\sqrt{5}+1\right|}{\sqrt{2}}\)
\(=\dfrac{\sqrt{2}\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}{\sqrt{2}}\) (vì \(\sqrt{5}+1>0\) )
`=5-1`
`=4`
c: \(=\left(\sqrt{3}-2\right)\left(\sqrt{3}+1\right)\sqrt{4+2\sqrt{3}}\)
=(căn 3-2)(4+2căn 3)
\(=4\sqrt{3}+6-8-4\sqrt{3}=-2\)
