Question

Racionalize: Favor responder com o passo a passo.

Answer 1

Explicação passo-a-passo:

a)

$\sf \dfrac{x^2y^3}{y\sqrt{x}}$

$\sf =\dfrac{x^2y^3}{y\sqrt{x}}\cdot\dfrac{\sqrt{x}}{\sqrt{x}}$

$\sf =\dfrac{x^2y^3\sqrt{x}}{xy}$

$\sf =xy^2\sqrt{x}$

b)

$\sf \dfrac{2}{3+\sqrt{3}}$

$\sf =\dfrac{2}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}$

$\sf =\dfrac{6-2\sqrt{3}}{3^2-(\sqrt{3})^2}$

$\sf =\dfrac{6-2\sqrt{3}}{9-3}$

$\sf =\dfrac{6-2\sqrt{3}}{6}$

$\sf =\dfrac{3-\sqrt{3}}{3}$

c)

$\sf \dfrac{7m}{\sqrt[4]{m^2}}$

$\sf =\dfrac{7m}{\sqrt[4]{m^2}}\cdot\dfrac{\sqrt[4]{m^2}}{\sqrt[4]{m^2}}$

$\sf =\dfrac{7m\sqrt[4]{m^2}}{m}$

$\sf =7\sqrt{m}$