Question

Determine whether $\sqrt[3]{327}$ is a surd or not.

• A. It is not a surd.
• B. It is a surd but not a quadratic surd.
• C. It is a quadratic surd.

Answer 1

The correct option is A It is not a surd.

Let's simplify $\sqrt[3]{327}.$

We know $27=3\times 3\times 3$

$\therefore \sqrt[3]{327}=\sqrt[3]{33\times 3\times 3}=(3^3{)}^{\frac{1}{3}}=\frac{3}{1}$

As it can be written in $\frac{p}{q},$ where $p$ and $q$ are integers, $q\ne 0$ and the ratio $\frac{p}{q}$ is in its reduced form, $\sqrt[3]{327}$ is a rational number.