A radical is a mathematical expression involving a root by means of a radical sign.
Some roots do not have real values; in this case, they are called undefined.
Even roots of negative numbers are undefined.
Evaluate the following radicals:
In a previous Concept, you learned how to evaluate rational exponents:
This can be written in radical notation using the following property.
You can also simplify other radicals, like cube roots and fourth roots.
Begin by finding the prime factorization of 135. This is easily done by using a factor tree.
Solution: This is read, “The fourth root of four to the second power.”
The fourth root of 16 is 2; therefore,
Sample explanations for some of the practice exercises below are available by viewing the following videos. Note that there is not always a match between the number of the practice exercise in the videos and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Radical Expressions with Higher Roots (8:46)
- For which values of n is −16−−−−√n undefined?
Evaluate each radical expression.
Write each expression as a rational exponent.
Write the following expressions in simplest radical form.