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 b^n = a, then b is the nth root of a.

Notation index radical radicand Note: An index of 2 is understood but not written in a square root sign.

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

Rational Exponents In other words, exponents that are fractions.

Definition of For any real number a and any integer n > 1, except when a < 0 and n is even

Examples:

Definition of Rational Exponents For any nonzero number b and any integers m and n with n > 1, except when b < 0 and n is even

NOTE: There are 3 different ways to write a rational exponent

Examples: