Question

Compare the following pair of surds:

$\sqrt{2},\sqrt[3]{35}$

• A. $\sqrt{2}<\sqrt[4]{45}$
• B. $\sqrt{3}<\sqrt[3]{35}$
• C. $\sqrt{2}<\sqrt[3]{35}$
• D. $\sqrt{2}<\sqrt[3]{33}$

Answer 1

Answer: (C)

$\sqrt{2}<\sqrt[3]{35}$

$\sqrt{2}=\sqrt[6]{62^3}=\sqrt[6]{68}$
$\sqrt[3]{35}=\sqrt[6]{65^2}=\sqrt[6]{625}$
$\sqrt[6]{68}<\sqrt[6]{625}$
$\sqrt{2}<\sqrt[3]{35}$