Răspuns:
[tex]2\sqrt{3}-1[/tex]
Explicație pas cu pas:
[tex]\sqrt{13-4\sqrt{3}}=\sqrt{13-\sqrt{48}}[/tex]
[tex]\sqrt{A-\sqrt{B}}=\sqrt{\frac{A+C}{2}}-\sqrt{\frac{A-C}{2}}\\C=\sqrt{A^{2}-B}[/tex]
A = 13
B = 48
C = [tex]\sqrt{13^{2}-48}=\sqrt{169-48}=\sqrt{121}=11[/tex]
[tex]\sqrt{13-\sqrt{48}}=\sqrt{\frac{13+11}{2}}-\sqrt{\frac{13-11}{2}}=\sqrt{\frac{\not24}{\not2}}-\sqrt{\frac{2}{2}}=[/tex] [tex]\sqrt{12}-\sqrt{1}=2\sqrt{3}-1[/tex]
