 Simplify

Section P.3

 How do we simplify expressions involving radicals and/or rational exponents?

 If a≥0 and b≥0 and b 2 = a, then b is the principal square root of a.

 If a≥0 and b≥0, then The square root of a product is the product of the square roots.

 Simplify Solution:

 Simplify

 If a≥0 and b>0, then The square root of the quotient is the quotient of the square roots.

 Simplify: Solution:

 Simplify: a)b)

 Read Section P.3  Page 32 #1-25 odd  Graphing calculator check-out ◦ Textbook window ◦ Need signed form ◦ Must have your ID or schedule

 Evaluate each expression in Exercises 1-6 or indicate that the root is not a real number.  Use the product rule to simplify the expressions in Exercises In Exercises 11-16, assume the variables represent nonnegative real numbers.

 Simplify

 We DO NOT leave radicals in the denominator  Multiply numerator and denominator by the smallest number that will eliminate the radical.  If square root: can multiply top and bottom by the radical in the denominator, then simplify

 For a denominator of form, we multiply numerator and denominator by its conjugate,

 If n, the index, is even, then a > 0 and b > 0. If n is odd, a and b can be any real numbers.

 For all real numbers, where the indicated roots represent real numbers,

 Read Section P.3  Page 32 #27-75 odd  You have until 1:50 to work on this assignment. We will then finish the P.3 notes.

 Rationalize and simplify

 The exponent m/n consists of two parts: the denominator n is the index of the radical and the numerator m is the exponent. Furthermore,

 Page 32 #77-93 odd, 104, 106, 121

 In Exercises 77-84, evaluate each expression without using a calculator.  In Exercises 85-94, simplify using properties of exponents.