The product is abbreviated where . The letter is called the exponent and the letter is called the base.
The principal nth root of is that the th root of which is if positive if is positive, and is negtive if is negative and is odd.
Thus,
The symbol is called a radical. Here is the index, is the radicand and is the radical sign. With principal square roots we usually omit the index and write instead of .
![\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.](https://s0.wp.com/latex.php?latex=%5Csqrt%5Bn%5D%7Bx%7D+%5Ctext%7B%5C%3A+is+%5C%3A%7D+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bll%7D+%5Ctext%7Bpositive+%5C%3A+if+%5C%3A%7D+x+%5Ctext%7B%5C%3A+is+%5C%3A+positive%7D+%5C%5C+%5Ctext%7Bnegative+%5C%3A+if+%5C%3A%7D+x+%5Ctext%7B%5C%3A+is+%5C%3A+negative+%5C%3A+and+%5C%3A%7D+n+%5Ctext%7B%5C%3A+is+%5C%3A+odd%7D+%5Cend%7Barray%7D%5Cright.&bg=T&fg=ffffff&s=0 "\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.")
![\sqrt[n]{x}](https://s0.wp.com/latex.php?latex=%5Csqrt%5Bn%5D%7Bx%7D&bg=T&fg=ffffff&s=0 "\sqrt[n]{x}")
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