Question

simplifique os radicais e efetue as operação 
(a) √12+√75+√108         (b)5√180+√245-17√5

 
. alguém?? ' 

Answer 1

Simplifique os radicais e efetue as operação
PARA SIMPLIFICAR temos que fatorar?????


(a) √12+√75+√108 

√12       12| 2                 √75               75| 3                 √108           108| 2
               6| 2                                      25| 5                                      54| 2
               3| 3                                        5| 5                                      27| 3
                  1                                           1                                          9| 3
                                                                                                           3| 3
                                                                                                             1
√12= 2√3                        √75 = 5√3                         √108=2².3³= 2².3².3¹=2.3√3= 6√3

√12+√75+√108    =    2√3 + 5√3 + 6√3   =   13√3


(b)5√180 + √245 -17√5

5√180  +  √245 - 17√5

5√180    180| 2                   √ 245    245| 5     
                90| 2                                  49| 7
                45| 3                                    7| 7
                15| 3                                        1   √245= 5.7.7=5¹.7²=  7√5
                  5| 5
                    1
 180 = 2.2.3.3.5= 2².3².5¹=
180 = 2.3√5 = 6√5

ENTÃO
5√180  +  √245 - 17√5  =
 5.6√5 + 7√5 - 17√5  =
30√5   +7√5  - 17√5 =
37√5 - 17√5    =   20√5