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 Definition of the Principal Square Root• If a is a nonnegative real number, the nonnegative number b such that b2 = a, denoted by is the principal square root of a. Square Roots of Perfect Squares The Product Rule for Square Roots • If a and b represent nonnegative real number, then • The square root of a product is the product of the square roots. Text Example • Simplify Solution: The Quotient Rule for Square Roots • If a and b represent nonnegative real numbers and b does not equal 0, then and • The square root of the quotient is the quotient of the square roots. Text Example• Simplify: Solution: Example • Perform the indicated operation: Solution: Example • Perform the indicated operation: Solution: Definition of the Principal nth Root of a Real Number means that • If n, the index, is even, then a is nonnegative (a≥ 0) and b is also nonnegative (b ≥ 0) . If n is odd, a and b can be any real numbers. Finding the nth Roots of Perfect nth PowersIf n is odd, If n is even an The Product and Quotient Rules for nth Roots • For all real numbers, where the indicated roots represent real numbers, and Definition of Rational Exponents Furthermore, Example• Simplify Solution: Definition of Rational Exponents • The exponent m/n consists of two parts: the denominator n is the root and the numerator m is the exponent. Furthermore, Radicals and Rational Exponents