Roots of real numbers and radical expressionsPresentation Transcript
5.5 Roots of Real Numbers and Radical Expressions
Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any positive integers n , if an = b , then a is the n th root of b .
Definitions A perfect square is the square of a natural number. 1, 4, 9, 16, 25, and 36 are the first six perfect squares. A perfect cube is the cube of a natural number. 1, 8, 27, 64, 125, and 216 are the first six perfect cubes.
Notation Note: An index of 2 is understood but not written in a square root sign. index radical radicand
Simplify To simplify means to find x in the equation: x 4 = 81 Solution: = 3
Principal Root The nonnegative root of a number Principal square root Opposite of principal square root Both square roots
Summary of Roots even odd one + root one - root one + root no - roots no real roots no + roots one - root one real root, 0
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.