Question

Racionalizar 10 / √18 + 2√2?

Answer 1

$<var>\frac{10}{\sqrt{18} + 2\sqrt{2}}</var>$

 

Se fatorarmos o √18

18 | 2

9   | 3

3   | 3

1

 

$<var>\sqrt{3^{2}*2} = 3\sqrt{2}</var>$

 

$<var>\frac{10}{3\sqrt{2} + 2\sqrt{2}}</var>$

 

$<var>\frac{10}{5\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}} = \frac{10\sqrt{2}}{5*2} = \frac{10\sqrt{2}}{10}</var>$

 

10 com 10 anula-se, ficando √2

 

$<var>\frac{10}{\sqrt{18} + 2\sqrt{2}} = \boxed{\sqrt{2}}</var>$