Question

1. Racionalize
a. 1/V2
b. 6/V10
c. V6 / V12
d. 2V2 / V20
e. 3V2 / V2+V3

Answer 1

Resposta:

Explicação passo-a-passo:

a. 1/V2*√2/√2=√2/2

b. 6/V10*√10/√10=6√10/10=>3√10/5

c. V6 / V12*√12/√12=>√72/12

d. 2V2 / V20* √20/√20=>2√40/20=>4√10/20=>√10/5

e. 3V2 / V2+V3* √2-√3/√2-√3

-6+3√6

Answer 2

Resposta:

Leia abaixo

Explicação passo-a-passo:

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

$\dfrac{6}{\sqrt{10}} = \dfrac{6}{\sqrt{10}} \times \dfrac{\sqrt{10}}{\sqrt{10}} = \dfrac{6\sqrt{10}}{(\sqrt{10})^2} = \dfrac{6\sqrt{10}}{10} = \dfrac{3\sqrt{10}}{5}$

$\dfrac{\sqrt{6}}{\sqrt{12}} = \dfrac{\sqrt{6}}{\sqrt{12}} \times \dfrac{\sqrt{12}}{\sqrt{12}} = \dfrac{\sqrt{72}}{(\sqrt{12})^2} = \dfrac{6\sqrt{2}}{12} = \dfrac{\sqrt{2}}{2}$

$\dfrac{2\sqrt{2}}{\sqrt{20}} = \dfrac{2\sqrt{2}}{\sqrt{20}} \times \dfrac{\sqrt{20}}{\sqrt{20}} = \dfrac{2\sqrt{40}}{(\sqrt{20})^2} = \dfrac{4\sqrt{10}}{20} = \dfrac{\sqrt{10}}{5}$

$\dfrac{3\sqrt{2}}{\sqrt{2} + \sqrt{3}} = \dfrac{3\sqrt{2}}{\sqrt{2} + \sqrt{3}} \times \dfrac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}} = \dfrac{6-3\sqrt{6}}{2-3} = 3\sqrt{6} -6$