Question

Racionalize conforme a imagem!

Answer 1

Explicação passo-a-passo:

2)

a)

$\sf \dfrac{x^3y}{8\sqrt{x}}\cdot\dfrac{\sqrt{x}}{\sqrt{x}}$

$\sf =\dfrac{x^3y\sqrt{x}}{8x}$

$\sf =\dfrac{x^2y\sqrt{x}}{8}$

b)

$\sf \dfrac{2}{9-\sqrt{5}}\cdot\dfrac{9+\sqrt{5}}{9+\sqrt{5}}$

$\sf =\dfrac{18+2\sqrt{5}}{9^2-(\sqrt{5})^2}$

$\sf =\dfrac{18+2\sqrt{5}}{81-5}$

$\sf =\dfrac{18+2\sqrt{5}}{76}$

$\sf =\dfrac{9+\sqrt{5}}{38}$

c)

$\sf \dfrac{4}{\sqrt[4]{5^2}}\cdot\dfrac{\sqrt[4]{5^2}}{\sqrt[4]{5^2}}$

$\sf =\dfrac{4\sqrt[4]{5^2}}{5}$

$\sf =\dfrac{4\sqrt[4]{25}}{5}$

Answer 2

Oie, Td Bom?!

a)

$= \frac{x {}^{3} y}{8 \sqrt{x} }$

$= \frac{x {}^{3} y}{8 \sqrt{x} } \: . \: \frac{ \sqrt{x} }{ \sqrt{x} }$

$= \frac{x {}^{3}y \sqrt{x} }{8 \sqrt{x} \sqrt{x} }$

$= \frac{x {}^{3} y \sqrt{x} }{8x}$

$= \frac{x {}^{2} y \sqrt{x} }{8}$

b)

$= \frac{2}{9 - \sqrt{5} }$

$= \frac{2}{9 - \sqrt{5} } \: . \: \frac{9 + \sqrt{5} }{ 9 + \sqrt{5} }$

$= \frac{2(9 + \sqrt{5} )}{(9 - \sqrt{5} ) \: . \: (9 + \sqrt{5} )}$

$= \frac{2(9 + \sqrt{5} )}{9 {}^{2} - \sqrt{5} {}^{2} }$

$= \frac{2(9 + \sqrt{5} )}{81 - 5}$

$= \frac{2(9 + \sqrt{5}) }{76}$

$= \frac{9 + \sqrt{5} }{38}$

c)

$= \frac{4}{ \sqrt[4]{5 {}^{2} } }$

$= \frac{4}{ \sqrt{5} }$

$= \frac{4}{ \sqrt{5} } \: . \: \frac{ \sqrt{5} }{ \sqrt{5} }$

$= \frac{4 \sqrt{5} }{ \sqrt{5} \sqrt{5} }$

$= \frac{4 \sqrt{5} }{5}$

Att. Makaveli1996