Understanding nth Roots
Suppose we know that . We want to find what number raised to the 3rd power is equal to 8. Since , we say that 2 is the cube root of 8. The nth root of is a number that, when raised to the nth power, gives . For example, is the 5th root of because . If is a real number with at least one nth root, then the principal nth root of is the number with the same sign as that, when raised to the nth power, equals . The principal nth root of is written as , where is a positive integer greater than or equal to 2. In the radical expression, is called the index of the radical.A General Note: Principal nth Root
If is a real number with at least one nth root, then the principal nth root of , written as , is the number with the same sign as that, when raised to the nth power, equals . The index of the radical is .Example 10: Simplifying nth Roots
Simplify each of the following:Solution
- because
- First, express the product as a single radical expression. because
Try It 10
Simplify.Licenses & Attributions
CC licensed content, Specific attribution
- College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface. License: CC BY: Attribution.