Question

Efectuati calcule:
$\sqrt{13 - 4 \sqrt{3} }$
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Answer 1

Răspuns:

   $2\sqrt{3}-1$

Explicație pas cu pas:

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

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

    A = 13

    B = 48

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

    $\sqrt{13-\sqrt{48}}=\sqrt{\frac{13+11}{2}}-\sqrt{\frac{13-11}{2}}=\sqrt{\frac{\not24}{\not2}}-\sqrt{\frac{2}{2}}=$ $\sqrt{12}-\sqrt{1}=2\sqrt{3}-1$