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The symbol $\sqrt{\hspace{3mm}}$ ; is called a radical. The origin of the radical symbol is the first letter ``r'' of the Latin word radix, which means ``root''.
There is other terminology that is related to radicals: In the expression $\sqrt[3]{x}$ $x$ is the radicand and $3$ is the index.
The index of a radical is usually an integer at least as large as two; however, if the index is two, it is usually not written. Moreover, if a radical does not have a written index, it is understood to be two, in which the case the radical denotes a square root.
A radical expression is an expression that involves a radical.
One can use fractional powers instead of the radical symbol via $\sqrt[n]{x} = x^{\frac{1}{n}}$ This practice of avoiding the radical symbol may be necessary due to typesetting issues.
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