Question

sendo a= (3+1/2) ao quadrado; e b=2+2/3
calcule a.b na forma irredutível

Answer 1

a= (3+1/2)  e  b=2+2/3  
 
Para (a .b):
$( \frac{6}{2} + \frac{1}{2} ) . ( \frac{6}{3} + \frac{2}{3} )$
$( \frac{7}{2}) . ( \frac{8}{3} )$
$\frac{7}{2} . \frac{8}{3} = \frac{56}{6}$
$\frac{28}{3}$

Agora, para (a².b):
$( \frac{6}{2} + \frac{1}{2} )^{2} . ( \frac{6}{3} + \frac{2}{3} )$

$( \frac{6}{2} + \frac{1}{2} )^{2}= ( \frac{6}{2} + \frac{1}{2} ) . ( \frac{6}{2} + \frac{1}{2} )$
$( \frac{6}{2} + \frac{1}{2} ) . ( \frac{6}{2} + \frac{1}{2} ) = \frac{36}{4} + \frac{6}{4} + \frac{6}{4} + \frac{1}{4} = \frac{37+12}{4} = \frac{49}{4}$

$\frac{49}{4} . ( \frac{6}{3} + \frac{2}{3} )$
$\frac{49}{4} . \frac{8}{3}$
$\frac{49}{4} . \frac{8}{3} = \frac{49}{1} . \frac{2}{3} = \frac{98}{3}$