\(1.\sqrt{2-\sqrt{3}}=\dfrac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{3-2\sqrt{3}+1}}{\sqrt{2}}=\dfrac{\text{ |}\sqrt{3}-1\text{ |}}{\sqrt{2}}=\dfrac{\sqrt{3}-1}{\sqrt{2}}\) \(2.\sqrt{15-\sqrt{13+\sqrt{48}}}=\sqrt{15-\sqrt{12+2.2\sqrt{3}+1}}=\sqrt{14-2\sqrt{3}}\) \(3.\sqrt{48-10\sqrt{7+4\sqrt{3}}}=\sqrt{48-10\sqrt{4+2.2\sqrt{3}+3}}=\sqrt{48-10\left(2+\sqrt{3}\right)}=\sqrt{28-10\sqrt{3}}=\sqrt{25-2.5\sqrt{3}+3}=5-\sqrt{3}\) \(4.\sqrt{5-\sqrt{13+4\sqrt{3}}}=\sqrt{5-\sqrt{12+2.2\sqrt{3}+1}}=\sqrt{4-2\sqrt{3}}=\sqrt{3-2\sqrt{3}+1}=\sqrt{3}-1\)
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