Question

Compare the following pairs of surds $\sqrt[8]{812},\sqrt[4]{46}$

• A. $\sqrt[8]{82}<\sqrt[4]{46}$
• B. $\sqrt[8]{88}<\sqrt[4]{46}$
• C. $\sqrt[8]{812}<\sqrt[4]{46}$
• D. $\sqrt[8]{812}<\sqrt[4]{44}$

Answer 1

Answer: (C)

$\sqrt[8]{812}<\sqrt[4]{46}$

$\sqrt[8]{812},\sqrt[4]{46}$
To compare, the order of the surds must be same.
$=>{12}^{\frac{1}{8}},6^{\frac{1}{4}}$
$=>{12}^{\frac{1}{8}},6^{\frac{2}{8}}$
$=>\sqrt[8]{812},\sqrt[8]{86^2}$
$=>\sqrt[8]{812},\sqrt[8]{836}$
Therefore
$=>12<36$
$=>\sqrt[8]{812}<\sqrt[8]{836}$
$=>\sqrt[8]{812}<\sqrt[4]{46}$