Question

Racionalize o denominador das expressões a seguir:
a) 3
_
√6

b) 1
____
2 + (Raiz de 2)


c) Raiz de 3
_________
raiz de 5

d) 2
_______
raiz de 2 + 1

e) Raiz de 3
_________
3- raiz de 3

Answer 1

$a)\\ {3\over\sqrt{6} }={3\sqrt{6} \over\sqrt{6} .\sqrt{6} }={3\sqrt{6} \over\sqrt{36} }={3\sqrt{6} \over6}={\sqrt{6} \over2}\\ \\ b)\\ {1\over2+\sqrt{2} }={1(2-\sqrt{2} )\over(2+\sqrt{2} )(2-\sqrt{2} }={2-\sqrt{2} \over4-\sqrt{4}}={2-\sqrt{2} \over4-2}={2-\sqrt{2} \over2}$

$c)\\ {\sqrt{3} \over\sqrt{5} }={\sqrt{3} .\sqrt{5} \over\sqrt{5} .\sqrt{5} }={\sqrt{15} \over\sqrt{25} }={\sqrt{15} \over5}\\ \\ d)\\ {2\over\sqrt{2} +1}={2(\sqrt{2} -1)\over(\sqrt{2} +1)(\sqrt{2} -1)}={2(\sqrt{2} -1)\over\sqrt{4}-1}={2(\sqrt{2} -1)\over2-1}={2\sqrt{2} -2\over1}$

$e)\\ {\sqrt{3} \over3-\sqrt{3}}={\sqrt{3} (3+\sqrt{3} )\over(3-\sqrt{3} )(3+\sqrt{3} )}=\\ \\ {3\sqrt{3} +\sqrt{9} \over9-\sqrt{9} }={3\sqrt{3} +3\over9-3}={3(\sqrt{3} +1)\over6}={\sqrt{3} +1\over2}$