Question

11. Rationalizează numitorii fracţiilor următoare:
2rad6/ rad3
-7rad13/rad26
4rad10/-rad24
15/2rad60​

Answer 1

Răspuns:

$\displaystyle \frac{2\sqrt{6} }{\sqrt{3} } \ = \ \frac{2\sqrt{6}\ \cdot \ \sqrt{3} }{\sqrt{3}\ \cdot \ \sqrt{3} } \ = \frac{2\sqrt{18} }{3} \ = \ \frac{2 \sqrt{9 \ \cdot 2} }{3} \ = \ \frac{2\ \cdot \ 3\sqrt{2} }{3} \ = \ 2\sqrt{2}$

$\displaystyle - \frac{7\sqrt{13} }{\sqrt{26} } \ =- \frac{7\sqrt{13} \ \cdot \sqrt{26} }{\sqrt{26} \ \cdot \ \sqrt{26} } = - \frac{7\sqrt{13} \ \cdot \sqrt{13 } \cdot \ \sqrt{2} }{ \ \ {26} } \ = - \ \frac{7\ \cdot \ 13 \ \cdot \ \sqrt{2} }{26} \ = \ - \frac{7\sqrt{2} }{2}$

$\displaystyle \frac{4\sqrt{10} }{ - \sqrt{24} } = \frac{4\sqrt{10} }{ - 2\sqrt{6} } \ = \ \frac{4\sqrt{10} \ \cdot \ \sqrt{6} }{ - 2\sqrt{6} \ \cdot \ \sqrt{6} } \ = \frac{ 4\sqrt{60} }{- \ 12} \ = \ \frac{ \sqrt{60} }{- \ 3}$

$\displaystyle \frac{ 15}{2\sqrt{60} } \ = \ \frac{ 15 \ \cdot \ \sqrt{60} }{2\sqrt{60} \ \cdot \ \sqrt{60} } = \ \frac{ 15 \ \cdot \ \sqrt{60} }{2 \ \cdot \ {60} } = \ \frac{ 15 \ \cdot \ 2 \sqrt{15} }{2 \ \cdot \ {60} } = \frac{\sqrt{15} }{4}$

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