Question

Extraia a raiz quadrada dos numeros a seguir pela decomposição em fatores primos:

a) $\sqrt{196}$
b) $\sqrt{256}$
c) $\sqrt{484}$
d) $\sqrt{729}$
e) $\sqrt{1600}$
f) $\sqrt{1024}$

Answer 1

$a) \sqrt{196} \to \sqrt{2^2*7^2} \to 2*7\to 14\\\\\\ b) \sqrt{256} \to \sqrt{2^2*2^2*2^2*2^2} \to 2*2*2*2\to 16\\\\\\ c) \sqrt{484} \to \sqrt{2^2*11^2} \to 2*11\to 22\\\\\\ d) \sqrt{729} \to \sqrt{3^2*3^2*3^2} \to 3*3*3\to 27\\\\\\ e) \sqrt{1600} \to \sqrt{2^2*2^2*2^2*5^2} \to 2*2*2*5\to 40\\\\\\ f) \sqrt{1024} \to \sqrt{2^2*2^2*2^2*2^2*2^2} \to 2*2*2*2*2\to 32$

Answer 2

a) => √196 = √(2.2.7.7) = √(2².7²) = 2.7 = 14

b) => √256 = √(2.2.2.2.2.2.2.2) = √(2².2².2².2²) = 2.2.2.2 = 16

c) => √484 = √(2.2.11.11) = √(2².11²) = 2.11 = 22

d) => √729 = √(3.3.3.3.3.3) = √(3².3².3²) = 3.3.3 = 27

e) => √1600 = √(2.2.2.2.2.2.5.5) = √(2².2².2².5²) = 2.2.2.5 = 40

f) => √1024 = √(2.2.2.2.2.2.2.2.2.2) = √(2².2².2².2².2²) = 2.2.2.2.2 = 32

Espero ter ajudado