Question

Is $\sqrt[3]{3296}$ an example of pure surd?

Answer 1

We know that a surd in which the whole of the rational number is under the radical sign and makes the radicand, is called pure surd.

In other words a surd having no rational factor except unity is called a pure surd.

Here, $\sqrt[3]{3296}$ can be rewritten as follows:

$\sqrt[3]{3296}=\sqrt[3]{32\times 2\times 2\times 37}=\sqrt[3]{32^3\times 37}=2\sqrt[3]{337}$

Since $\sqrt[3]{3296}$ is reducible.

Hence, $\sqrt[3]{3296}$ is not a pure surd.