Question

Racionalize: a) 3/√2

b)√8/√5

c)8√7/5√2

d)15/²√7²

e)18/$\sqrt[4]{6}$

f)1/4³√2
POR FAVOR ME AJUDA!

Answer 1

isso é racionalização de denominador

A)
$\frac{3}{ \sqrt{2} } = \frac{3}{ \sqrt{2} } \times \frac{ \sqrt{2} }{2} =$
$\frac{3 \times \sqrt{2} }{( \sqrt{2}) {}^{2} } = \frac{3 \times \sqrt{2} }{ \sqrt{2 {}^{2} } } = \frac{3 \times \sqrt{2} }{2}$
B)
$\frac{8}{ \sqrt{5} } = \frac{ \sqrt{8} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } =$
$\frac{ \sqrt{8 \times 2} }{( \sqrt{5} ) {}^{2} } = \frac{ \sqrt{40} }{ \sqrt{ {5}^{2} } } =$
fatora o 40:
40 |2
20 |2
10. |2
5. |5
1
$\frac{ \sqrt{40} }{ \sqrt{ {5}^{2} } } = \frac{ \sqrt{ {2}^{2} \times 2 \times 5 } }{5} = \frac{2 \sqrt{2 \times 5} }{5}$
$\frac{2 \sqrt{10} }{5}$

C)
$\frac{8 \sqrt{7} }{5 \sqrt{2} } = \frac{8 \sqrt{7} }{5 \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } =$
$\frac{8 \sqrt{7 \times 2} }{(5 \sqrt{2}) {}^{2} } = \frac{8 \sqrt{14} }{5 \sqrt{2 {}^{2} } } = \frac{8 \sqrt{2} }{5 \sqrt{4} }$
$\frac{8 \sqrt{14} }{5 \times 2} = \frac{8 \sqrt{14} }{10} \div 2 =$
$\frac{4 \sqrt{2} }{5}$
D)
$\frac{15}{ \sqrt[2]{ {7}^{2} } } = \frac{15}{7}$
E)
$\frac{18}{ \sqrt[4]{6} } = \frac{18}{ \sqrt[4]{6} } \: \times \frac{ \sqrt[4]{ {6}^{3} } }{ \sqrt[4]{ {6}^{3} } } =$
$\frac{18 \sqrt[4]{ {6}^{3} } }{ \sqrt[4]{ {6}^{1} \times {6}^{3} }} = \frac{18 \sqrt[4]{ {6}^{3} } }{ \sqrt[4]{ {6}^{1 + 3} } } = \frac{18 \sqrt[4]{ {6}^{3} } }{ \sqrt[4]{ {6}^{4} } }$
$\frac{18 \sqrt[4]{ {6}^{3} } }{6}$
simplifica o 18 e o 6:
$3 \sqrt[4]{ {6}^{3} }$

F)
$\frac{1}{4 \sqrt[3]{2} } = \frac{1}{4 \sqrt[3]{2} } \times \frac{ \sqrt[3]{ {2}^{2} } }{ \sqrt[3]{ {2}^{2} } } = \frac{1 \times \sqrt[3]{ {2}^{2} } }{4 \times ( \sqrt[3]{2} \times \sqrt[3]{ {2}^{2} }) }$
$\frac{1 \sqrt[3]{ {2}^{2} } }{4( \sqrt[3]{ {2}^{1 + 2} }) } = \frac{1 \sqrt[3]{ {2}^{2} } }{4 \sqrt[3]{ {2}^{3} } } = \frac{1 \sqrt[3]{ {2}^{2} } }{4 \sqrt[3]{ {2}^{3} } } = \frac{ \sqrt[3]{ {2}^{2} } }{4 \times 2}$
$\frac{1 \sqrt[3]{ {2}^{2} } }{8} = \frac{1 \sqrt[3]{ {4}^{} } }{8}$