Question

Racionalize os denominadores das seguintes frações:
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Answer 1

Explicação passo-a-passo:

$a)\\ \\ {4\over\sqrt{7} }={4\sqrt{7} \over\sqrt{7} .\sqrt{7} }={4\sqrt{7} \over\sqrt{49}} ={4\sqrt{7} \over7}$

$b)\\ \\ {\sqrt{3} \over\sqrt{5} }={\sqrt{3} .\sqrt{5} \over\sqrt{5} .\sqrt{5} }={\sqrt{15} \over\sqrt{25} }={\sqrt{15} \over5}$

$c)\\ \\ {3(2-\sqrt{5} )\over(2+\sqrt{5} )(2-\sqrt{5} )}=\\ \\ {3.(2-\sqrt{5} )\over2^2-(\sqrt{5} )^2}=\\ \\{ 3.(2-\sqrt{5} )\over4-5}=\\ \\{ 3.(2-\sqrt{5} )\over-1}=\\ \\ -3(2-\sqrt{5} )=-6+3\sqrt{5}$

$d)\\ \\ {2.(\sqrt{3} -\sqrt{5} )\over(\sqrt{3} +\sqrt{5} )(\sqrt{3} -\sqrt{5} )}=\\ \\ {2(\sqrt{3} -\sqrt{5} )\over(\sqrt{3})^2-(\sqrt{5} )^2}=\\ \\ {2(\sqrt{3} -\sqrt{5} )\over3-5}=\\ \\ {\not2.(\sqrt{3} -\sqrt{5} )\over-\not2}=\\ \\ -(\sqrt{3} -\sqrt{5} )=-\sqrt{3} +\sqrt{5}$