\(\sqrt{6-2\sqrt{5}}+\sqrt{8+2\sqrt{15}}-\sqrt{3}\\ =\sqrt{5-2\sqrt{5}+1}+\sqrt{5-2\sqrt{15}+3}-\sqrt{3}\\ =\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot1+1^2}+\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}-\sqrt{3}\\ =\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}-\sqrt{3}\\ =\left|\sqrt{5}-1\right|+\left|\sqrt{5}-\sqrt{3}\right|-\sqrt{3}\\ =\sqrt{5}-1+\sqrt{5}-\sqrt{3}-\sqrt{3}\\ =2\sqrt{5}-2\sqrt{3}-1\)
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