\(\sqrt{4-2\sqrt{3}}-\sqrt{4+2\sqrt{3}}=\sqrt{3-2\sqrt{3}+1}-\sqrt{3+2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(\sqrt{3}+1\right)^2}=\left(\sqrt{3}-1\right)-\left(\sqrt{3}+1\right)=-2\)\(\sqrt{9-2\sqrt{20}}+\sqrt{14+2\sqrt{45}}=\sqrt{9-2\sqrt{2^2.5}}+\sqrt{14+2\sqrt{3^2.5}}=\sqrt{9-2.2\sqrt{5}}+\sqrt{14+2.3\sqrt{5}}=\sqrt{5-4\sqrt{5}+4}+\sqrt{9+6\sqrt{5}+5}=\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{5}+3\right)^2}=\left(\sqrt{5}-2\right)+\left(\sqrt{5}+3\right)=1+2\sqrt{5}\)\(\sqrt{9-2\sqrt{20}}+\sqrt{6+2\sqrt{5}}=\sqrt{5-4\sqrt{5}+4}+\sqrt{5+2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}=\left(\sqrt{5}-2\right)+\left(\sqrt{5}+1\right)=-1+2\sqrt{5}\)
\(\sqrt{12+3\sqrt{7}}-\sqrt{12-3\sqrt{7}}=\sqrt{\left(\sqrt{12+3\sqrt{7}}-\sqrt{12-3\sqrt{7}}\right)^2}=\sqrt{12+3\sqrt{7}-2\sqrt{\left(12+3\sqrt{7}\right)\left(12-3\sqrt{7}\right)}+12-3\sqrt{7}}=\sqrt{24-2\sqrt{144-9.7}}=\sqrt{24-2.9}=\sqrt{6}\)
a: \(=\sqrt{3}-1-\sqrt{3}-1=-2\)
b: \(=\sqrt{5}-2+3+\sqrt{5}=2\sqrt{5}+1\)
c: \(=\sqrt{5}-2+\sqrt{5}+1=2\sqrt{5}-1\)
d: \(=\dfrac{\sqrt{24+6\sqrt{7}}-\sqrt{24-6\sqrt{7}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{21}+\sqrt{3}-\sqrt{21}+\sqrt{3}}{\sqrt{2}}=\dfrac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\)
