Question

√2-√3/√6+√3-√4/√12+√4-√5/√20+√5-√6/√30=
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Answer 1

Răspuns:

1. fractiile se simplifica prin numaratorul lor

2. se rationalizeaza numitorii

3. se aduce la acelasi numitor si se fac operatiile de adunare si scadere

$\sqrt{2} -\frac{\sqrt{3}}{\sqrt{6} } +\sqrt{3} -\frac{\sqrt{4}}{\sqrt{12} } +\sqrt{4} -\frac{\sqrt{5}}{\sqrt{20} } +\sqrt{5} -\frac{\sqrt{6}}{\sqrt{30} } =$

$=\sqrt{2} -\frac{1}{\sqrt{2} } +\sqrt{3} -\frac{1}{\sqrt{3} } +\sqrt{4} -\frac{1}{\sqrt{4} } +\sqrt{5} -\frac{1}{\sqrt{5} } =$

$=\sqrt{2} -\frac{\sqrt{2}}{2} +\sqrt{3} -\frac{\sqrt{3} }{3} +2 -\frac{1}{2} +\sqrt{5} -\frac{{\sqrt{5} }}{5} =$

$= \frac{30\sqrt{2} -15\sqrt{2} +30\sqrt{3} -10\sqrt{3} +60 -15 +30\sqrt{5} -6\sqrt{5} }{30}=$

$= \frac{15\sqrt{2} +20\sqrt{3} +45 +24\sqrt{5} }{30}$

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