Answer :
as [tex] \sqrt[3]{8}=2 [/tex]
so [tex] \sqrt[3]{6}<2[/tex]
try 1.9 | 1.9³=6.859
try 1.95 | 1.95³=7.414875
it is greater
try 1.85 | 1.85³=6.331625
make more less
1.815³=5.979018375 then
so 1.82³=6.028568=6 (.app)
now as u know that [tex]2^8=256[/tex]
so [tex] \sqrt[8]{12} [/tex] must lie between 1 and 2
and it must be close to 1
1.2⁸=4.3 (.app)
1.3⁸=8 (.app)
so it must be close to 1.35 which is less than 1.85
so i can say that
[tex] \sqrt[3]{6}< \sqrt[8]{12} [/tex]
so [tex] \sqrt[3]{6}<2[/tex]
try 1.9 | 1.9³=6.859
try 1.95 | 1.95³=7.414875
it is greater
try 1.85 | 1.85³=6.331625
make more less
1.815³=5.979018375 then
so 1.82³=6.028568=6 (.app)
now as u know that [tex]2^8=256[/tex]
so [tex] \sqrt[8]{12} [/tex] must lie between 1 and 2
and it must be close to 1
1.2⁸=4.3 (.app)
1.3⁸=8 (.app)
so it must be close to 1.35 which is less than 1.85
so i can say that
[tex] \sqrt[3]{6}< \sqrt[8]{12} [/tex]