Question

Racionalize o denominador : .

a) 1/4+√2
b) 2/√5+2
c) √3/√3-1
d) -1/7-√2

Answer 1

$\frac{1}{4 + \sqrt{2} } = \frac{4 + \sqrt{2} }{(4 + \sqrt{2})(4 - \sqrt{2}) } = \frac{4 + \sqrt{2} }{14}$

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

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


  Fator Racionalizante: 7 + √2

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