Question

Compare the following pair of surds:

$\sqrt[3]{32},\sqrt[6]{63}$

• A. $\sqrt[3]{32}>\sqrt[6]{65}$
• B. $\sqrt[5]{52}>\sqrt[6]{63}$
• C. $\sqrt[3]{32}>\sqrt[6]{63}$
• D. $\sqrt[3]{32}>\sqrt[6]{62}$

Answer 1

The correct option is C $\sqrt[3]{32}>\sqrt[6]{63}$

$\sqrt[3]{32},\sqrt[6]{63}$
To compare, the order of the surds must be same.
$=>2^{\frac{1}{3}},3^{\frac{1}{6}}$
$=>2^{\frac{2}{6}},3^{\frac{1}{6}}$
$=>\sqrt[6]{64},\sqrt[6]{63}$
Therefore
$=>4>3$
$=>\sqrt[6]{64}>\sqrt[6]{63}$
$=>\sqrt[3]{32}>\sqrt[6]{63}$