Question

Simplifique a expressão:
√2 . (√126 + √56) - √3 . (√84-√3+48)

Answer 1

√2 (√126 + √56) - √3.( √84 - √3 + 48)
√2 (3√14 + 2√14) - √3.(2√21 - √3 + 48)
√2.(5√14) - √3.(2√21 - √3 + 48)
 5√28        - 2.√63 + 3 - 48√3
5.2√7        - 2.3√7 + 3 - 48√3  
10√7         - 6√7   + 3 - 48√3

= 4√7 - 48√3 + 3
**********************************************
Fatoração:

63: 3
21: 3
7: 7
1     =  √9.√7 = 3√7

--------------------------------------------
28: 2
14: 2
7: 7
1        =  √4.√7 = 2√7
____________________________

126: 2
63: 3
21: 3
7: 7
1       =  √9.√14 = 3√14
------------------------------------------------------
56: 2
28: 2
14: 2
7: 7
1          √4.√14 = 2√14
------------------------------------------------------
84: 2
42: 2
21: 3
7: 7
1        =  √4.√21 = 2√21
-------------------------------------------------------
48: 2
24: 2
12: 2
6: 2
3: 3
1       =   √16.√3 = 4√3

Answer 2

√2.(√126+√56) -√3.(√84-√3+√48)=

√2.(3√14+2√14) - √3.(2 √21- √3+4 √3)=

√2.5. √14-√3.(2 √21+3 √3)=

√28.5-2 √63-9=

2 √7.5-2.3 √7-9=

10 √7-6 √7-9=

4 √7-9