Radical Operator

The radical operator returns the -th root of the provided expression. For example, the cube root of inline equals , because .

The radical operator is closely related to exponentiation and logarithms. In a hypothetical scenario of exponential population growth starting from an initial value of , the relationship between exponentiation, logarithms, and radicals can be expressed as follows.

Equation Operator
Exponent
Given the growth rate and the time elapsed , the exponent operator returns the population .
Logarithm
Given the growth rate and the population , the logarithm operator returns the time elapsed .
Radical
Given the time elapsed and the population , the radical operator returns the growth rate .

Radical Notation

The radical operator with the written above the radical sign is equivalent to raising the expression to the power. While radicals and fractional exponents are mathematically equivalent, radical notation is commonly used for readability and to emphasize the concept of “taking a root.”

When no number is provided above the radical sign then the square root operation is implied, meaning that .

Practice

What is ?
What is the -th root of ?
What is the -rd root of ?

Related Operators

The exponentiation operator is a binary operator. The base is an expression or number that is being raised to some exponent. The exponent expression is denoted using superscript text.

Taking the logarithm of a number is the inverse operation of exponentiation. The subscript number is the base of the logarithm and the expression is the operand.