Question

$\sqrt{13-4\sqrt{3} }$ cum se rezolva, explicati va rog

Answer 1

Răspuns:

    $2\sqrt{3}-1$

Explicație pas cu pas:

    $\sqrt{13-4\sqrt{3}}=\sqrt{13-\sqrt{48}}$

    $\sqrt{13^{2}-48}=\sqrt{169-48}=\sqrt{121}=11$

    $\sqrt{13-\sqrt{48}}=\sqrt{\frac{13+11}{2}}-\sqrt{\frac{13-11}{2}}=\sqrt{12}-1=2\sqrt{3}-1$

Formula aplicata:

    $\sqrt{A\pm\sqrt{B}}=\sqrt{\frac{A+C}{2}}\pm\sqrt{\frac{A-C}{2}}$

    $C=\sqrt{A^{2}-B}\\C\in\mathbb N$