6.1 Roots and Radical     Expressions
Powers and Roots• Corresponding to every power there is a root.  – Examples:    If          , then    If          , then  ...
The nth Root• If         , with a and b real numbers and n a  positive integer, then a is an nth root of b  If n is odd…  ...
Vocabulary• You use a radical sign   to indicate a root• The number or term under the radical sign is  called the radicand...
Finding all Roots• To find the roots of a number, ask yourself  “What raised to the n power, gives the  radicand?”  – To f...
Example: Find all the real roots   Find all the real cube roots of each number1. 10002. 0.0083.   1   27
Example: Find all the real roots   Find all the real fourth roots of each number1. 12. -0.00013.   16   81
Example: Find each Root1.   3         8     42.       1             23.       2
nth Roots of nth Powers                          n       n                                      a if n is oddFor any real ...
Simplifying Radicals• Break the radical down into perfect powers of  n.  – Remember Exponent Rules!
Example: Simplify               41.       81x2.       16x   8     3    6 93.       ab
Example: Simplify     3    12 151.       a b          8 122.   4         x y     4   12    163.       x y
Example (p364)Some teachers adjust test scores when a testis difficult. One teacher’s formula for adjustingscores is A 10 ...
Homework• P364 #1 – 30 all, 37
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6.1

  1. 1. 6.1 Roots and Radical Expressions
  2. 2. Powers and Roots• Corresponding to every power there is a root. – Examples: If , then If , then If , then
  3. 3. The nth Root• If , with a and b real numbers and n a positive integer, then a is an nth root of b If n is odd… If n is even… There is one real nth root of b And b is positive, there are two ( + )real nth roots of b. • The positive root is the principle root: • The negative root is its opposite: And b is negative, there are no real nth roots of b.
  4. 4. Vocabulary• You use a radical sign to indicate a root• The number or term under the radical sign is called the radicand• The index gives the degree of the root. n a
  5. 5. Finding all Roots• To find the roots of a number, ask yourself “What raised to the n power, gives the radicand?” – To find the roots of a fraction, consider the numerator and denominator separately – Don’t forget about Positive and Negative numbers
  6. 6. Example: Find all the real roots Find all the real cube roots of each number1. 10002. 0.0083. 1 27
  7. 7. Example: Find all the real roots Find all the real fourth roots of each number1. 12. -0.00013. 16 81
  8. 8. Example: Find each Root1. 3 8 42. 1 23. 2
  9. 9. nth Roots of nth Powers n n a if n is oddFor any real number a, a a if n is even It is important to remember this rule, especially when working with variables!
  10. 10. Simplifying Radicals• Break the radical down into perfect powers of n. – Remember Exponent Rules!
  11. 11. Example: Simplify 41. 81x2. 16x 8 3 6 93. ab
  12. 12. Example: Simplify 3 12 151. a b 8 122. 4 x y 4 12 163. x y
  13. 13. Example (p364)Some teachers adjust test scores when a testis difficult. One teacher’s formula for adjustingscores is A 10 R where A is the adjustedscore and R is the raw score. If the raw scoreson one test range from 36 to 90, what is therange of adjusted scores?
  14. 14. Homework• P364 #1 – 30 all, 37
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