Question

Racionalize o denominador das frações

a) 1/$\sqrt{2}$

b) 2/$\sqrt{3}$

c) 4/2$\sqrt{2}$

d)$\sqrt{2}$/($\sqrt{2} + 1)$

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Answer 1

Explicação passo-a-passo:

a)

$\sf \dfrac{1}{\sqrt{2}}$

$\sf =\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf =\dfrac{\sqrt{2}}{2}$

b)

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

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

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

c)

$\sf \dfrac{4}{2\sqrt{2}}$

$\sf =\dfrac{4}{2\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf =\dfrac{4\sqrt{2}}{2\cdot2}$

$\sf =\dfrac{4\sqrt{2}}{4}$

$\sf =\sqrt{2}$

d)

$\sf \dfrac{\sqrt{2}}{\sqrt{2}+1}$

$\sf =\dfrac{\sqrt{2}}{\sqrt{2}+1}\cdot\dfrac{\sqrt{2}-1}{\sqrt{2}-1}$

$\sf =\dfrac{2-\sqrt{2}}{(\sqrt{2})^2-1^2}$

$\sf =\dfrac{2-\sqrt{2}}{2-1}$

$\sf =\dfrac{2-\sqrt{2}}{1}$

$\sf =2-\sqrt{2}$