Question

Racionalize o denominador de:

Answer 1

$a) \frac{1}{ \sqrt{2} } \\ \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{2} }{2}$

$b) \frac{2}{ \sqrt{10} } \\ \frac{2}{ \sqrt{10} } \times \frac{ \sqrt{10} }{ \sqrt{10} } = \frac{2 \sqrt{10} }{ 10 } = \frac{ \sqrt{10} }{5}$

$c) \frac{3}{ \sqrt{15} } = \frac{3}{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{3 \sqrt{15} }{15} = \frac{ \sqrt{15} }{5}$

$d) \: \frac{5}{3 \sqrt{3} } = \frac{5}{3 \sqrt{3} } \times \frac{3 \sqrt{3} }{3 \sqrt{3} } = \frac{15 \sqrt{3} }{9 \times 3} = \frac{15 \sqrt{3} }{27} \\ \frac{5 \sqrt{3} }{9}$

$e) \frac{15}{2 \sqrt{5} } = \frac{15}{2 \sqrt{5} } \times \frac{2 \sqrt{5} }{2 \sqrt{5} } = \frac{30 \sqrt{5} }{20} = \frac{3 \sqrt{5} }{2}$

$f) \frac{25}{6 \sqrt{30} } = \frac{25}{6 \sqrt{30} } \times \frac{6 \sqrt{30} }{6 \sqrt{30} } = \frac{150 \sqrt{30} }{1080} = \frac{5 \sqrt{30} }{36}$

$g) \frac{20}{ \sqrt{10} } = \frac{20}{ \sqrt{10} } \times \frac{ \sqrt{10} }{ \sqrt{10} } = \frac{20 \sqrt{10} }{10} = \frac{2 \sqrt{10} }{1}$

$h) \frac{ \sqrt{5} }{ \sqrt{2} } = \frac{ \sqrt{5} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{5 \times 2} }{2} = \frac{ \sqrt{10} }{2}$