When the index of the radical is EVEN, and the exponent of the variable outside the radical is ODD, and the there is no variable inside the radical, then an absolute value is needed. When the index of the radical is EVEN, and the exponent of the variable outside the radical and the exponent inside the radical is ODD, then no absolute value is needed. (See Figure 3-2.) Figure 3-1 with Absolute Value (See Figure 3-1.) If the absolute value were not present, then the result of the expression would contain negative values. When the index of the radical and the exponent inside the radical is EVEN, and the exponent of the variable outside the radical is ODD, then an absolute value is needed. When the index of the radical is EVEN and the exponent of the variable outside the radical is EVEN, then no absolute value is needed regardless of the exponent inside the radical. When the index of the radical is ODD, then no absolute value is needed regardless of the exponent of the variable outside or inside the radical. NOTE: Any even-numbered root must be a positive number otherwise, it is imaginary. Therefore, all we need to look at is if the index of the radical is EVEN, and the exponent of the variable inside the radical is EVEN or there is no variable left inside the radical once the radical is simplified. (See the table Simplifying Radicals.) CaseĪs you can see from the table above, there are only two cases where the absolute value is needed when simplifying a radical: Case 3 and Case 5. When working with radical expressions this requirement does not apply to any odd root because odd roots exist for negative numbers. This ensures that the answer is positive. If the problem expresses that the result must be a positive number, then the absolute value must be used when simplifying radical expressions with variables. If a problem does not indicate that the result be positive, then you need to assume that we are dealing with both positive and negative real numbers. The above example assumes that the result is a positive real number. Suppose we simplified a radical expression with the results shown below.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |