Question

determine a raiz quadrada exata dos seguintes numeros:
a) 324
b) 961
c) 1936
d) 1225
e) 676
f) 529
g) 1024
h) 1089

Answer 1

a)
√324 = 18

324: 2
162: 2
81: 3
27: 3
9: 3
3: 3
-------
1   = 2².3².3² = 2.3.3 = 6.3 = 18
******************************************

b)
√961 = 31

961: 31
31: 31
----------
1    =     √31² = 31

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c) 
√1936 = 44

1936: 2
968: 2
484: 2
242: 2
121: 11
11: 11
-------------
1           =  2².2².11² = 2.2.11 = 4.11 = 44


¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d) 
√1225  = 35

1225: 5
245: 5
49: 7
7: 7
----------
1        5².7²  = 5.7 = 35


¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e) √676 = 26

676 :2
338: 2
169: 13
13: 13
--------------
1    = 2².13² = 2.13 = 26

f)
529: 23
23: 23
------------
1   =  √23² =   23

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
√1024  = 32

1024: 2
512: 2
256: 2
128: 2
64: 2
32:2
16: 2
8: 2
4: 2
2: 2
-----------
1     =   2¹º =  2⁴.2⁴.2² = √16.√16.√4 = 4.4.2 = 16.2 = 32

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
h)
√1089 = 33


1089: 3
363: 3
121: 11
11: 11
---------------
1    = 3².11² = 3.11 = 33