Question

Introduza nos radicais seus fatores externos

a)3√10
b)5 ³√6
c)4√5
d)10 ³√10
e)6√11
f)3√5
h)5√3
i)15√2

Answer 1

a) √10 x 9= √90
b) ∛6 x 5³=∛ 6 x 125= ∛750
c)√5 x 16= √80
d)∛10 x 10³= ∛10 x 1000=∛10.000
e)√11 x 36=√396
f)√5 x 3²=√5 x 9= √45
h)√3 x 25=√75
i)√2 x 225= √450

Answer 2

Introduzindo fatores externos em radicais de índice n:

$a\sqrt[n]{b}=\sqrt[n]{a^{n}}\sqrt[n]{b}\\a\sqrt[n]{b}=\sqrt[n]{a^{n}\cdot b}$
_______________________

a)

$3\sqrt{10}=3\sqrt[2]{10}\\3\sqrt{10}=\sqrt{3^{2}\cdot10}\\3\sqrt{10}=\sqrt{9\cdot10}\\3\sqrt{10}=\sqrt{90}$

b)

$5\sqrt[3]{6}=\sqrt[3]{5^{3}\cdot6}\\5\sqrt[3]{6}=\sqrt[3]{125\cdot6}\\5\sqrt[3]{6}=\sqrt[3]{750}$

c)

$4\sqrt[2]{5}=\sqrt{4^{2}\cdot5}\\4\sqrt[2]{5}=\sqrt{16\cdot5}\\4\sqrt[2]{5}=\sqrt{80}$

d)

$10\sqrt[3]{10}=\sqrt[3]{10^{3}\cdot10}\\10\sqrt[3]{10}=\sqrt[3]{10^{4}}\\10\sqrt[3]{10}=\sqrt[3]{10000}$

e)

$6\sqrt[2]{11}=\sqrt{6^{2}\cdot11}\\6\sqrt[2]{11}=\sqrt{36\cdot11}\\6\sqrt[2]{11}=\sqrt{396}$

f)

$3\sqrt[2]{5}=\sqrt{3^{2}\cdot5}\\3\sqrt[2]{5}=\sqrt{9\cdot5}\\3\sqrt[2]{5}=\sqrt{45}$

g)

$5\sqrt{3}=\sqrt{5^{2}\cdot3}\\5\sqrt{3}=\sqrt{25\cdot3}\\5\sqrt{3}=\sqrt{75}$

h)

$15\sqrt[2]{2}=\sqrt{15^{2}\cdot2}\\15\sqrt[2]{2}=\sqrt{225\cdot2}\\15\sqrt[2]{2}=\sqrt{450}$