Question

Racionalize os denominadores:
$\frac{4}{ \sqrt{15} }$

$\frac{9}{ \sqrt{6} }$

$\frac{6}{5 \sqrt{22} }$

$\frac{8}{10+ \sqrt{3} }$

(com conta)

Answer 1

$a) \frac{4}{ \sqrt{15} } = \\ \\ \frac{4* \sqrt{15} }{ \sqrt{15}* \sqrt{15} } }= \\ \\ \frac{4* \sqrt{15} }{ \sqrt{15 ^{2} } } } = \\ \\ \frac{4 \sqrt{15} }{15}$



$b) \frac{9}{ \sqrt{6} } = \\ \\ \frac{9* \sqrt{6} }{ \sqrt{6}* \sqrt{6} }= \\ \\ \frac{9 \sqrt{6} }{\sqrt{6 ^{2} } }= \\ \\ \frac{9 \sqrt{6} }{6} = \\ \\ \frac{3 \sqrt{6} }{2}$



$c) \frac{6}{5 \sqrt{22} } = \\ \\ \frac{6* \sqrt{22} }{5 \sqrt{22}* \sqrt{22} } \\ \\ \frac{6 \sqrt{22} }{5 \sqrt{22 ^{2} } } = \\ \\ \frac{6 \sqrt{22} }{5*22} = \\ \\ \frac{6 \sqrt{22} }{110} = \\ \\ \frac{3 \sqrt{22} }{55}$



$d) \frac{8}{10+ \sqrt{3} } = \\ \\ \frac{8*(10- \sqrt{3}) }{(10+ \sqrt{3})*(10- \sqrt{3}) } = \\ \\ \frac{8*(10- \sqrt{3}) }{(10 ^{2} - \sqrt{3 ^{2} }) }= \\ \\ \frac{8*(10- \sqrt{3}) }{100 - 3 } }= \\ \\ \frac{8*(10- \sqrt{3} )}{97} = \\ \\ \frac{80-8 \sqrt{3} }{97}$