Question

Racionalize os denominadores de:

Answer 1

Fiz num papel,pois pelo tabela seria bem mais trabalhoso. Espero ter ajudado.

Answer 2

Oie, Td Bom?!

a)

$\frac{13a}{ \sqrt[3]{a {}^{2} } } = \frac{13a}{ \sqrt[3]{a {}^{2} } } \: . \: \frac{ \sqrt[3]{a} }{ \sqrt[3]{a} } = \frac{13a \sqrt[3]{a} }{ \sqrt[3]{a {}^{2} } \sqrt[3]{ a} } = \frac{13a \sqrt[3]{a} }{ \sqrt[3]{a {}^{2} \: . \: a }} = \frac{13a \sqrt[3]{a} }{ \sqrt[3]{a {}^{3} } } = \frac{13a \sqrt[3]{a} }{a} = 13\sqrt[3]{a}$

b)

$\frac{t}{ \sqrt[5]{t} } = \frac{t}{ \sqrt[5]{t} } \: . \: \frac{ \sqrt[5]{t {}^{4} } }{ \sqrt[5]{t {}^{4} } } = \frac{t \sqrt[5]{t {}^{4} } }{ \sqrt[5]{t} \sqrt[5]{t {}^{4} } } = \frac{t \sqrt[5]{t {}^{4} } }{ \sqrt[5]{t \: . \: t {}^{4} } } = \frac{t \sqrt[5]{t {}^{4} } }{t} = \sqrt[5]{t {}^{4} }$

c)

$\frac{15r}{ \sqrt[4]{3r} } = \frac{15r}{ \sqrt[4]{3r} } \: . \: \frac{ \sqrt[4]{(3r) {}^{3} } }{ \sqrt[4]{(3r) {}^{3} } } = \frac{15r \sqrt[4]{(3r) {}^{3} } }{ \sqrt[4]{3r} \sqrt[4]{(3r) {}^{3} } } = \frac{15r \sqrt[4]{(3r) {}^{3} } }{ \sqrt[4]{3r \: . \: (3r) {}^{3} } } = \frac{15r \sqrt[4]{(3r) {}^{3} } }{ \sqrt[4]{3r \: . \: 27r {}^{3} } } = \frac{15r \sqrt[4]{(3r) {}^{3} } }{ \sqrt[4]{81r {}^{4} } } = \frac{15r \sqrt[4]{(3r) {}^{3} } }{3r} = 5 \sqrt[4]{(3r) {}^{3} } = 5 \sqrt[4]{27r {}^{3} }$

d)

$\frac{18x \sqrt[3]{x} }{ \sqrt[3]{x {}^{2} } } = \frac{18x }{ \sqrt[3]{x} } = \frac{18x}{ \sqrt[3]{x} } \: . \: \frac{ \sqrt[3]{x {}^{2} } }{ \sqrt[3]{x {}^{2} } } = \frac{18x \sqrt[3]{x {}^{2} } }{ \sqrt[3]{x} \sqrt[3]{x {}^{2} } } = \frac{18x \sqrt[3]{x {}^{2} } }{ \sqrt[3]{x \: . \: x {}^{2} } } = \frac{18x \sqrt[3]{x {}^{2} } }{ \sqrt[3]{x {}^{3} } } = \frac{18x \sqrt[3]{x {}^{2} } }{x} = 18 \sqrt[3]{x {}^{2} }$

e)

$\frac{25mx}{ \sqrt[4]{mx {}^{2} } } = \frac{25mx}{ \sqrt[4]{mx {}^{2} } } \: . \: \frac{ \sqrt[4]{(mx {}^{2} ) {}^{3} } }{ \sqrt[4]{(mx {}^{2} ) {}^{3} } } = \frac{25mx \sqrt[4]{(mx {}^{2}) {}^{3} } }{ \sqrt[4]{mx {}^{2} } \sqrt[4]{(mx {}^{2} ) {}^{3} } } = \frac{25mx \sqrt[4]{(mx {}^{2} ) {}^{3} } }{ \sqrt[4]{mx {}^{2} \: . \: (mx {}^{2} ) {}^{3} } } = \frac{25m \sqrt[4]{(mx {}^{2} ) {}^{3} } }{ \sqrt[4]{mx {}^{2}m {}^{3} x {}^{6} } } = \frac{25mx \sqrt[4]{(mx {}^{2}) {}^{3} } }{ \sqrt[4]{m {}^{4} x {}^{8} } } = \frac{25mx \sqrt[4]{(mx {}^{2} ) {}^{3} } }{mx {}^{2} } = \frac{25 \sqrt[4]{(mx {}^{2} ) {}^{3} } }{x} = \frac{25 \sqrt[4]{m {}^{3}x {}^{6} } }{x} = \frac{25x \sqrt[4]{m {}^{3}x {}^{2} } }{x} = 25 \sqrt[4]{m {}^{3} x {}^{2} }$

f)

$\frac{15 \sqrt[5]{m {}^{2} } }{ \sqrt[5]{2m {}^{3} } } = \frac{15}{ \sqrt[5]{2m} } = \frac{15}{ \sqrt[5]{2m} } \: . \: \frac{ \sqrt[5]{(2m) {}^{4} } }{ \sqrt[5]{(2m) {}^{4} } } = \frac{15 \sqrt[5]{(2m) {}^{4} } }{ \sqrt[5]{2m} \sqrt[5]{(2m) {}^{4} } } = \frac{15 \sqrt[5]{16m {}^{4} } }{ \sqrt[5]{2m \: . \: (2m) {}^{4} } } = \frac{15 \sqrt[5]{16m {}^{4} } }{ \sqrt[5]{2m \: . \: 16m {}^{4} } } = \frac{15 \sqrt[5]{16m {}^{4} } }{ \sqrt[5]{32m {}^{5} } } = \frac{15 \sqrt[5]{16m {}^{4} } }{2m}$

g)

$\frac{ \sqrt{ a} }{ \sqrt[4]{a {}^{3} } } = \frac{a {}^{ \frac{1}{2} } }{ a {}^{ \frac{3}{4} } } = \frac{1}{a {}^{ \frac{1}{4} } } = \frac{1}{ \sqrt[4]{a} } = \frac{1}{ \sqrt[4]{a} } \: . \: \frac{ \sqrt[4]{a {}^{3} } }{ \sqrt[4]{a {}^{3} } } = \frac{1 \sqrt[4]{a {}^{3} } }{ \sqrt[4]{ a} \sqrt[4]{a {}^{3} } } = \frac{ \sqrt[4]{a {}^{3} } }{ \sqrt[4]{a \: . \: a {}^{3} } } = \frac{ \sqrt[4]{a {}^{3} } }{ \sqrt[4]{a {}^{4} } } = \frac{ \sqrt[4]{a {}^{3} } }{a}$

h)

$\frac{m \sqrt{x} }{ \sqrt[6]{m {}^{5} } } = \frac{m \sqrt{x} }{ \sqrt[6]{m {}^{5} } } \: . \: \frac{ \sqrt[6]{m} }{ \sqrt[6]{m} } = \frac{m \sqrt{x} \sqrt[6]{m} }{ \sqrt[6]{m {}^{5} } \sqrt[6]{m} } = \frac{m \sqrt{x} \sqrt[6]{m} }{ \sqrt[6]{m {}^{5} \: . \: m } } = \frac{m \sqrt{x} \sqrt[6]{m} }{ \sqrt[6]{m {}^{6} } } = \frac{m \sqrt{x} \sqrt[6]{m} }{m} = \sqrt{x} \sqrt[6]{m} = \sqrt[6]{mx {}^{3} }$

Att. Makaveli1996