Question

Extraer todos los factores posibles de los siguientes radicales :
a) √8
b) √50
c) √12
d)√300
e) √180
f)√392
g) 3√56
h) 3√192
i) 4√64
j) 4√112
k) 4√162
L) 3√500

Answer 1

$a) \sqrt{8}= \sqrt{2^3}= \sqrt{2^2.2}= 2\sqrt{2}\\ b)\sqrt{50} = \sqrt{2.25} = \sqrt{2.5^2} = 5\sqrt{2} \\ c)\sqrt{12} = \sqrt{3.4} = \sqrt{3.2^2} = 2\sqrt{3} \\ d)\sqrt{300} = \sqrt{3.100} = \sqrt{3.10^2} = 10\sqrt{3}=\\ e) \sqrt{180} = \sqrt{5.36} = \sqrt{5.6^2} = 6\sqrt{5} \\ f)\sqrt{392} = \sqrt{2.196} = \sqrt{2.14^2} = 14\sqrt{2} \\ g)3\sqrt{56} = 3\sqrt{4.14} = 3\sqrt{2^.14} = 3.2\sqrt{14}=6 \sqrt{14}$
$h)3\sqrt{192} = 3\sqrt{3.64} = 3\sqrt{3.8^2} = 3.8\sqrt{3}=24 \sqrt{3} \\ i)4\sqrt{64} = 4\sqrt{8^2} = 4.8 =32\\ j)4\sqrt{112} =4\sqrt{7.16} =4\sqrt{7.4^2} = 4.4\sqrt{7}=16 \sqrt{7} \\ k)4\sqrt{162} =4\sqrt{2.81} =4\sqrt{2.9^2} =4.9\sqrt{2}=36 \sqrt{2} \\ l) 3\sqrt{500} = 3\sqrt{5.100} = 3\sqrt{5.10^2} = 5.10\sqrt{5} =50 \sqrt{5}$