Question

Which is greater - $\sqrt[3]{6}$ or $\sqrt[8]{12}$
Solve and then tell....

Answer 1

as $\sqrt[3]{8}=2$
so $\sqrt[3]{6}<2$
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 $2^8=256$
so $\sqrt[8]{12}$ 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
$\sqrt[3]{6}< \sqrt[8]{12}$