Question

40 PONTOS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! raionalize os denominadores:a)$\frac{10}{\sqrt{5} }$; b)$\frac{2\sqrt{2} }{\sqrt{3} }$; c)$\frac{9}{2\sqrt{3} }$

Answer 1

Oie, Td Bom?!

a)

$= \frac{10}{ \sqrt{5} }$

$= \frac{10}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} }$

$= \frac{10 \sqrt{5} }{ \sqrt{5} \sqrt{5} }$

$= \frac{10 \sqrt{5} }{5}$

$= 2 \sqrt{5}$

b)

$= \frac{2 \sqrt{2} }{ \sqrt{3} }$

$= \frac{2 \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} }$

$= \frac{2 \sqrt{2} \sqrt{3} }{ \sqrt{3} \sqrt{3} }$

$= \frac{2 \sqrt{6} }{3}$

c)

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

$= \frac{9}{2 \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} }$

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

$= \frac{9 \sqrt{3} }{2 \times 3}$

$= \frac{9 \sqrt{3} }{6}$

$= \frac{3 \sqrt{3} }{2}$

Att. Makaveli1996

Answer 2

Explicação passo-a-passo:

a)

$\sf \dfrac{10}{\sqrt{5}}$

$\sf =\dfrac{10}{\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}$

$\sf =\dfrac{10\sqrt{5}}{5}$

$\sf =\red{2\sqrt{5}}$

b)

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

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

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

c)

$\sf \dfrac{9}{2\sqrt{3}}$

$\sf =\dfrac{9}{2\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf =\dfrac{9\sqrt{3}}{2\cdot3}$

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