2009
10.28

The product $x \cdot x \cdot x$ is abbreviated $x^{3} = x^{n}$ where $n = 3$. The letter $n$ is called the exponent and the letter $x$ is called the base.

The principal nth root of $x$ is that the $n$th root of $x$ which is if positive if $x$ is positive, and is negtive if $x$ is negative and $n$ is odd.

Thus,

$\sqrt[n]{x} \text{\: is \:} \left\{\begin{array}{ll} \text{positive \: if \:} x \text{\: is \: positive} \\ \text{negative \: if \:} x \text{\: is \: negative \: and \:} n \text{\: is \: odd} \end{array}\right.$

The symbol $\sqrt[n]{x}$ is called a radical. Here $n$ is the index, $x$ is the radicand and $\sqrt{}$ is the radical sign. With principal square roots we usually omit the index and write $\sqrt{x}$ instead of $\sqrt[n]{x}$.