Question

Compare the following pairs of surds. $\sqrt[4]{464},\sqrt[6]{6128}$

• A. $\sqrt[4]{464}>\sqrt[6]{6128}$
• B. $\sqrt[4]{464}<\sqrt[6]{6128}$
• C. $\sqrt[4]{464}\ne \sqrt[6]{6128}$
• D. $\sqrt[4]{464}=\sqrt[6]{6128}$

Answer 1

The correct option is A $\sqrt[4]{464}>\sqrt[6]{6128}$

$\sqrt[4]{464}=\sqrt[4]{42^6}=2\sqrt[4]{42^2}=2\sqrt{2}=2\sqrt[6]{62^3}=2\sqrt[6]{68}$
$\sqrt[6]{6128}=\sqrt[6]{62^7}=2\sqrt[6]{62}$
$\sqrt[4]{464}>\sqrt[6]{6128}$