Question

If the surds $\sqrt{3}$, $\sqrt[4]{46}$, $\sqrt[8]{812}$ and $\sqrt[16]{1624}$ are written in descending order, then the arrangement is

• A. $\sqrt[4]{46}$, $\sqrt[8]{812}$, $\sqrt[16]{1624}$, $\sqrt{3}$
• B. $\sqrt[4]{46}$, $\sqrt[16]{1624}$, $\sqrt{3}$, $\sqrt[8]{812}$
• C. $\sqrt{3}$, $\sqrt[4]{46}$, $\sqrt[8]{812}$, $\sqrt[16]{1624}$
• D. $\sqrt[16]{1624}$, $\sqrt{3}$, $\sqrt[4]{46}$, $\sqrt[8]{812}$

Answer 1

The correct option is C $\sqrt{3}$, $\sqrt[4]{46}$, $\sqrt[8]{812}$, $\sqrt[16]{1624}$

$\sqrt{3}$, $\sqrt[4]{46}$, $\sqrt[8]{812}$, $\sqrt[16]{1624}$
LCM of the order 2,4,8, and 16 $=$ 16
$\sqrt[16]{163^8}$, $\sqrt[16]{166^4}$, $\sqrt[16]{16{12}^2}$, $\sqrt[16]{1624}$
$\sqrt[16]{166561}$, $\sqrt[16]{161296}$, $\sqrt[16]{16144}$, $\sqrt[16]{1624}$