Question

Simplificação de radicais: Primeiro decomponha em fatores primos e depois simplifique: m)$\sqrt \frac{8}{27}$ f) $\sqrt \frac{2}{9}$

Answer 1

Explicação passo-a-passo:

m)

8 | 2

4 | 2

2 | 2

1

8 = 2³

27 | 3

9 | 3

3 | 3

1

27 = 3³

$\sf \sqrt{\dfrac{8}{27}}$

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

$\sf =\sqrt{\dfrac{2^2\cdot2}{3^2\cdot3}}$

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

$\sf =\dfrac{2\sqrt{6}}{3\cdot3}$

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

f)

9 | 3

3 | 3

1

9 = 3²

$\sf \sqrt{\dfrac{2}{9}}$

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

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

Answer 2

Resposta:

$m)\frac{ 2\sqrt{5} }{9}$

$f) \frac{\sqrt{2} }{3}$

Explicação passo-a-passo:

$m)\sqrt{\frac{8}{27} }=\frac{\sqrt{8} }{\sqrt{27} } =\frac{2\sqrt{2} }{3\sqrt{3} } =\frac{2\sqrt{2} .3\sqrt{3} }{3\sqrt{3} .3\sqrt{3} }=\frac{6\sqrt{6} }{9\sqrt{9} } =\frac{6\sqrt{6}}{9.3} =\frac{2\sqrt{6}}{9}$

$f)\sqrt{\frac{2}{9} }=\frac{\sqrt{2} }{\sqrt{9} } =\frac{\sqrt{2} }{3}$