Question

rationalizati numitorii fractiilor:
a)
$\frac{12}{ \sqrt{6 - \sqrt{2} } }$

$\frac{4}{ \sqrt{7 - \sqrt{5} } }$
$\frac{8}{ \sqrt{6 + \sqrt{2} } }$
$\frac{6}{ \sqrt{5 - \sqrt{2} } }$

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Answer 1

Explicație pas cu pas:

$\frac{12}{ \sqrt{6}- \sqrt{2} }$ =$\frac{12( \sqrt{6} + \sqrt{2}) }{6 - 2} = \frac{12( \sqrt{6} + \sqrt{2} ) }{4} = 3( \sqrt{6} + \sqrt{2} ) = 3 \sqrt{6} + 3 \sqrt{2}$

$\frac{4}{ \sqrt{7}- \sqrt{5} }$ = $\frac{4( \sqrt{7} + \sqrt{5} ) }{2} = 2( \sqrt{7} + \sqrt{5} ) = 2 \sqrt{7} + \sqrt{5}$

$\frac{8}{ \sqrt{6} + \sqrt{2} }$ =$\frac{8( \sqrt{6} - \sqrt{2}) }{4} = 2( \sqrt{6} - \sqrt{2} ) = 2 \sqrt{6} - 2 \sqrt{2}$

$\frac{6}{ \sqrt{5}- \sqrt{2} }$ =$\frac{6( \sqrt{5} - \sqrt{2}) }{3 } = 2 \sqrt{5} - 2\sqrt{2}$