Question

Classify the following into like surds:
$\sqrt[3]{324},\sqrt[3]{381},\sqrt[3]{3108},\sqrt[3]{3192},\sqrt[3]{32916}$

Answer 1

Let us first write all of them in their simplest form:
$\sqrt[3]{324}=2\sqrt[3]{33},\sqrt[3]{381}=3\sqrt[3]{33},\sqrt[3]{3108}=3\sqrt[3]{34},\sqrt[3]{3192}=4\sqrt[3]{33},\sqrt[3]{32916}=9\sqrt[3]{34}$.
We can make two groups of like surds: $\{2\sqrt[3]{33},3\sqrt[3]{33},4\sqrt[3]{33}\}$ and $\{3\sqrt[3]{34},9\sqrt[3]{34}\}$. Thus we get two groups of like or similar surds:
$\{\sqrt[3]{324},\sqrt[3]{381},\sqrt[3]{3192}\}$ and $\{\sqrt[3]{3108},\sqrt[3]{32916}\}$.