Resposta/Explicação passo a passo:
Dica: Fatore o número dentro da raiz. E responda sua atividade!!!!!!!!
a) [tex]\sqrt[3]{1}[/tex]
Fatorando 1:
[tex]1 = 1. 1.1 = 1^{3}[/tex]
Logo:
[tex]\sqrt[3]{1^{3} } = 1[/tex]
b) [tex]\sqrt[3]{125}[/tex]
[tex]125 = 5.5.5 = 5^{3} \\\sqrt[3]{5^{3} } = 5[/tex]
c)[tex]\sqrt[3]{64}[/tex]
[tex]64 = 2.2.2.2.2.2 = 2^{6} \\\sqrt[3]{2^{6} } = 2^{2} = 4[/tex]
d)[tex]\sqrt[3]{216}[/tex]
[tex]216 = 2.2.2.3.3.3 = 2^{3} . 3^{3} \\\sqrt[3]{2^{3} . 3^{3}} = 2.3 = 6[/tex]
e)[tex]\sqrt[3]{1000}[/tex]
[tex]1000 = 2.2.2.5.5.5 = 2^{3} . 5^{3}\\\sqrt[3]{2^{3} . 5^{3}} = 2.5 = 10[/tex]
f)[tex]\sqrt[3]{343}[/tex]
[tex]343 = 7.7.7 = 7^{3}\\\sqrt[3]{7^{3} }[/tex]
g)[tex]\sqrt[3]{0}[/tex]
[tex]0 = 0.0.0 = 0^{3} \\\sqrt[3]{0^{3}} = 0[/tex]
h)[tex]\sqrt[4]{16}[/tex]
[tex]16 = 2.2.2.2 = 2^{4} \\\sqrt[4]{2^{4} } = 2[/tex]
i)[tex]\sqrt[5]{32}[/tex]
[tex]32 = 2.2.2.2.2 = 2^{5} \\\sqrt[5]{2^{5} } = 2[/tex]
j)[tex]\sqrt[4]{625}[/tex]
[tex]625 = 5.5.5.5 = 5^{4} \\\sqrt[4]{5^{4} } = 5[/tex]
k)[tex]\sqrt[7]{128}[/tex]
[tex]128 = 2.2.2.2.2.2.2 = 2^{7} \\\sqrt[7]{ 2^{7} } = 2[/tex]
l)[tex]\sqrt[8]{256}[/tex]
[tex]256 = 2.2.2.2.2.2.2.2 = 2^{8} \\\sqrt[8]{ 2^{8} } = 2[/tex]
m)[tex]\sqrt[6]{729}[/tex]
[tex]729 = 3.3.3.3.3.3 = 3^{6} \\\sqrt[6]{3^{6} } = 3[/tex]
n)[tex]\sqrt[4]{10000}[/tex]
[tex]10000 = 10.10.10.10 = 10^{4} \\\sqrt[4]{10^{4} } = 10[/tex]
o)[tex]\sqrt[3]{512}[/tex]
[tex]512 = 8 . 8 .8 = 8^{3} \\\sqrt[3]{8^{3}} = 8[/tex]
p)[tex]\sqrt[9]{0}[/tex]
[tex]0.0.0.0.0.0.0.0.0 = 0^{9} \\\sqrt[9]{0^{9} } = 0[/tex]