A radical is used to represent the square root of a number. For example, ...
[tex]\sqrt{2}[/tex]
represents the square root of 2, a value that, when multiplied by itself, gives 2.
A radical with an index (n) is used to represent the n-th root of a number. For example, ...
[tex]\sqrt[5]{3}[/tex]
represents the 5th root of 3. The product of this number with itself a total of 5 times gives 3.
Either of these roots can be represented using fractional exponents:
[tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]
[tex]\sqrt[5]{3}=3^{\frac{1}{5}}[/tex]
