Roots of real numbers and radical expressions
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This document defines roots and radical expressions. It defines a square root as a number that produces another number when squared, and defines an nth root as a number that produces another number when raised to the nth power. It discusses notation for radicals, simplifying radicals, principal roots, and examples of taking roots of variable expressions and using absolute value signs with radicals.
Roots of real numbers and radical expressions
- 1. Roots of Real Numbers and Radical Expressions
- 2. Definition of Square Root For any real numbers a and b, if , then a is a square root of b. Ex: , 5 is a square root of 25
- 3. Definition of n th Root For an real numbers a and b, and any positive n, if , then a is an nth root of b. EX: Since , 2 is a fifth root of 32.
- 4. Notation Note: An index of 2 is understood but not written in a square root sign. index radical radicand
- 5. Simplify To simplify means to find x in the equation: x 4 = 81 Solution: = 3
- 6. Principal Root The nonnegative root of a number Principal square root Opposite of principal square root Both square roots
- 7. Summary of Roots even odd one + root one - root one + root no - roots no real roots no + roots one - root one real root, 0
- 8. Examples
- 9. Examples
- 10. Taking n th roots of variable expressions Using absolute value signs If the index ( n ) of the radical is even, the power under the radical sign is even, and the resulting power is odd, then we must use an absolute value sign.
- 11. Examples Even Even Even Even Odd Odd
- 12. Even Even Odd Odd Even Even 2