Question

Racionalize as questões a seguir:
A. 7/3√5
B. 1/√6 - 2

Answer 1

racionalizar

a)
$\frac{7}{3 \sqrt{5} } = \\ \\ fator~~ racionalizante~~ \sqrt{5} \\ \\ \frac{7 \sqrt{5} }{3( \sqrt{5}. \sqrt{5}) } = \\ \\ \frac{7 \sqrt{5} }{3. \sqrt{5^2} } = \\ \\ \frac{7 \sqrt{5} }{3.5} = \\ \\ \frac{7 \sqrt{5} }{15}$

b)
$\frac{1}{ \sqrt{6}-2 } = \\ \\ fator~~racionalizante~~ \sqrt{6} +2 \\ \\ \frac{ \sqrt{6}+2 }{( \sqrt{6}+2)( \sqrt{6}-2) } = \\ \\ \frac{ \sqrt{6}+2 }{ \sqrt{6^2}-2^2 } = \\ \\ \frac{ \sqrt{6}+2 }{6-4} \\ \\ \frac{ \sqrt{6}+2 }{2} \\ \\ ou \\ \\ \frac{ \sqrt{6} }{2} + \frac{2}{2} = \frac{ \sqrt{6} }{2} +1$