Question

Extraia a raiz quadrada de cada número a seguir pela decomposição em fatores primos

A)256 b)196 c)484 d)729 e)1600 f)1024

Answer 1

Vamos lá.

a) √256 =  √2×√2×√2×√2 =2×2×2×2=16

256/2
128/2
64/2
32/2
16/2
8/2
4/2
2/2
1  ==256 = 2^8.

b) √196 = √2×√7 = 2 × 7 = 14

196/2
98/2
49/7
7/7
1==========196 = 2².7²

c) √484 = √2 × √11 = 2 × 11 = 22

484/2
242/2
121/11
11/11
1=========484 = 2² × 11²

d) √729 = √3 × √3 × √3 = 3 × 3 × 3 = 27

729/3
243/3
81/3
27/3
9/3
3/3
1=======729 = 3^6

e) √1600 = √2 × √2 × √2 × √5 = 2 × 2 × 2 × 5 = 40

1600/2
800/2
400/2
200/2
100/2
50/2
25/5
5/5
1=========1600 = 2^6 × 5²

f) √1024 = √2 × √2 × √2 × √2 × √2 = 2 × 2 × 2 × 2 × 2 = 32

1024/2
512/2
256/2
128/2
64/2
32/2
16/2
8/2
4/2
2/2
1========1024 = 2^10.

Espero ter ajudado