Question

raționalizați numitori și calculați​

Answer 1

Răspuns:

a) $\frac{\sqrt{5} }{30}$

b)  $\frac{3\sqrt{7} }{14}$

c)  $\frac{11\sqrt{2} }{12}$

d)  $\frac{31\sqrt{2} }{30}$

Explicație pas cu pas:

a)  $\frac{2}{3\sqrt{5} } - \frac{1}{2\sqrt{5} } = \frac{2\sqrt{5} }{3\sqrt{5}*\sqrt{5} } - \frac{\sqrt{5} }{2\sqrt{5} *\sqrt{5} } = \frac{2\sqrt{5} }{15} - \frac{\sqrt{5} }{10} = \frac{4\sqrt{5}-3\sqrt{5} }{30} = \frac{\sqrt{5} }{30}$

b)  $\frac{2}{3\sqrt{7} } + \frac{5}{6\sqrt{7} } = \frac{2\sqrt{7} }{21} + \frac{5\sqrt{7} }{42} = \frac{4\sqrt{7} + 5\sqrt{7} }{42} = \frac{9\sqrt{7} }{42} = \frac{3\sqrt{7} }{14}$

c)  $\frac{3}{2\sqrt{2} } + \frac{1}{3\sqrt{2} } = \frac{3\sqrt{2} }{4} + \frac{\sqrt{2} }{6} = \frac{9\sqrt{2} + 2\sqrt{2} }{12} = \frac{11\sqrt{2} }{12}$

d)  $\frac{2}{3\sqrt{2} } + \frac{7}{5\sqrt{2} } = \frac{2\sqrt{2} }{6} + \frac{7\sqrt{2} }{10} = \frac{5*2\sqrt{2} + 3*7\sqrt{2} }{30} = \frac{10\sqrt{2} + 21\sqrt{2} }{30} = \frac{31\sqrt{2} }{30}$