a/ \(M=\sqrt{3-2\sqrt{3}+1}+\sqrt{27}=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{27}\)
=\(\sqrt{3}-1+\sqrt{27}\)=\(4\sqrt{3}-1\)
b/\(K=\sqrt{5-2\sqrt{5}+1}-5\sqrt{5}+1\)
=\(\sqrt{\left(\sqrt{5}-1\right)^2}\)-\(5\sqrt{5}+1\)=\(\sqrt{5}\)-1-5\(\sqrt{5}\)+1=-4\(\sqrt{5}\)
c/\(Q=\sqrt{2-2\sqrt{2}+1}-\sqrt{2+2\sqrt{2}+1}\)
=\(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(\sqrt{2}+1\right)^2}\)
=\(\sqrt{2}-1-\sqrt{2}-1\)=-2
a) M=\(\sqrt{4-2\sqrt{3}}-\sqrt{27}\)
=\(\sqrt{\left(1+\sqrt{3}\right)^2}\)\(-\sqrt{27}\)
=\(1+\sqrt{3}-\sqrt{27}\)\(\left(1+\sqrt{3}\ge O\right)\)
=1+ \(\sqrt{3}-3\sqrt{3}\)
=1-2\(\sqrt{3}\)
b) K=\(\sqrt{6-2\sqrt{5}}\)\(-\sqrt{20}-3\sqrt{5}+1\)
= \(\sqrt{\left(1-\sqrt{5}\right)^2}-2\sqrt{5}-3\sqrt{5}+1\)
=\(\sqrt{5}-1-5\sqrt{5}+1\)
=\(-4\sqrt{5}\)
c) Q= \(\sqrt{3-2\sqrt{2}-}\)\(\sqrt{3+2\sqrt{2}}\)
= \(\sqrt{\left(1-\sqrt{2}\right)^2}-\sqrt{\left(1+\sqrt{2}\right)^2}\)
=\(\sqrt{2}-1\left(\sqrt{2}+1\right)\)
=\(\sqrt{2}-1-\sqrt{2}-1\)
=\(-2\)
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