Question

Compare the following pairs of surds. $\sqrt{3},\sqrt[3]{32}$

• A. $\sqrt{3}<\sqrt[3]{32}$
• B. $\sqrt{3}\ne \sqrt[3]{32}$
• C. $\sqrt{3}>\sqrt[3]{32}$
• D. $\sqrt{3}=\sqrt[3]{33}$

Answer 1

Answer: (C)

$\sqrt{3}>\sqrt[3]{32}$

$\sqrt{3}=\sqrt[6]{63^2}=\sqrt[6]{69}$
$\sqrt[3]{32}=\sqrt[6]{62^2}=\sqrt[6]{64}$
$\sqrt[6]{69}>\sqrt[6]{64}$
$\sqrt{3}>\sqrt[3]{32}$