Question

4. Racionalize:
a)
$\frac{2}{ \sqrt{} 6}$
b)
$\frac{2}{3 \sqrt{2} }$
c)
$\frac{1}{3 + \sqrt{3} }$
d)
$\frac{7}{ \sqrt{10 - \sqrt{3} } }$
e)
$\frac{ \sqrt{3} }{ \sqrt{3 - 1} }$
​

Answer 1

Resposta:

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Explicação passo a passo:

Answer 2

$a) \\ \frac{2}{ \sqrt{6} } \\ \frac{2}{ \sqrt{6} } \: . \: \frac{ \sqrt{6} }{ \sqrt{6} } \\ \frac{2 \sqrt{6} }{ \sqrt{6} \sqrt{6} } \\ \frac{2 \sqrt{6} }{6} \\ \boxed{\boxed{\boxed{ \frac{ \sqrt{6} }{3} }}}$

$b) \\ \frac{2}{3 \sqrt{2} } \\ \frac{2}{3 \sqrt{2} } \: . \: \frac{ \sqrt{2} }{ \sqrt{2} } \\ \frac{2 \sqrt{2} }{3 \sqrt{2} \sqrt{2} } \\ \frac{2 \sqrt{2} }{3 \: . \: 2} \\ \frac{2 \sqrt{2} }{6} \\ \boxed{\boxed{\boxed{ \frac{ \sqrt{2} }{3} }}}$

$c) \\ \frac{1}{3 + \sqrt{3} } \\ \frac{1}{3 + \sqrt{3} } \: . \: \frac{3 - \sqrt{3} }{3 - \sqrt{3} } \\ \frac{1(3 - \sqrt{3}) }{(3 + \sqrt{3} ) \: . \: (3 - \sqrt{3}) } \\ \frac{3 - \sqrt{3} }{9 - 3} \\ \boxed{\boxed{\boxed{ \frac{3 - \sqrt{3} }{6} }}}$

$d) \\ \frac{7}{ \sqrt{10 - \sqrt{3} } } \\ \frac{7}{ \sqrt{10 - \sqrt{3} } } \: . \: \frac{ \sqrt{10 - \sqrt{3} } }{ \sqrt{10 - \sqrt{3} } } \\ \frac{7 \sqrt{10 - \sqrt{10} } }{ \sqrt{10 - \sqrt{3} } \sqrt{10 - \sqrt{3} } } \\ \frac{7 \sqrt{10 - \sqrt{3} } }{10 - \sqrt{3} } \\ \frac{7 \sqrt{10 - \sqrt{3} } }{10 - \sqrt{3} } \: . \: \frac{10 + \sqrt{3} }{10 + \sqrt{3} } \\ \frac{7 \sqrt{10 - \sqrt{3} }(10 + \sqrt{3}) }{(10 - \sqrt{3}) \: . \: (10 + \sqrt{3} )} \\ \frac{70 \sqrt{10 - \sqrt{3} } + 7 \sqrt{(10 - \sqrt{3}) \: . \: 3 } }{100 - 3} \\ \boxed{\boxed{\boxed{ \frac{70 \sqrt{10 - \sqrt{3} } + 7 \sqrt{30 - 3 \sqrt{3} } }{97} }}}$

$e) \\ \frac{3}{ \sqrt{3 - 1} } \\ \frac{3}{ \sqrt{2} } \\ \frac{3}{ \sqrt{2} } \: . \: \frac{ \sqrt{2} }{ \sqrt{2} } \\ \frac{3 \sqrt{2} }{ \sqrt{2} \sqrt{2} } \\ \boxed{\boxed{\boxed{ \frac{3 \sqrt{2} }{2} }}}$

atte. yrz