6. 1 roots and Radical Expressions 6 6.1 roots and Radical Expressions 6.2 Multiplying and Dividing Radical Expressions Algebra II w/ trig

The square root of a number and squaring a number are inverses of each other. indicates the nth root n is the index(if there is not a number there, it is an understood 2), # is the radicand, √ is the radical sign Square Root: if , then a is the square root of b. nth root: if then a is an nth root of b.

If n is odd There is one real nth root of b If n is even And b is positive, there are two real nth roots of b. The positive root is the principal root , the nth root of b. The negative root is its opposite, or negative the nth root of b. And b is negative, there are no real nth roots of b.

Property : nth Roots of nth Powers For any real number a, Example:

Find all the real roots of each number. Real Squares 25 0.36 -64 Real Cubes 81 0.008

II. Simplify. Use absolute value symbols when needed. C. D.

E. F. G.

III. Find two real solutions for each equation. 1. 2. 3.

6.2 Multiplying and Dividing Radical Expressions I. Properties of Square Roots: A. Product Property of Square Roots If a and b are real numbers and n>1: B. Quotient Property of Square Roots

II. Simplify. A. B. C. D.

III. Multiply or Divide, if possible. Then simplify. A. B. C. D.

Rationalize – to eliminate radical from a part of a fractional expression Generally, you would rationalize a denominator, but you may be asked to rationalize the numerator. So, when not stated always rationalize your denominator. To rationalize you must multiply the term(s) by something that causes it to become a perfect root, so the radical can be eliminated. Example: To eliminate from a denominator, you would need to multiply by . Then their product would be which can be simplified to 3xy, thus eliminating the radical.

IV. Rationalize the numerator and denominator of each IV. Rationalize the numerator and denominator of each. (You can divide first when possible.) A . B. √ C. D.

Homework Pre-AP p. 365 #11-55 odd P. 371 #11-51 odd, 52 You may check your answers in the back of the book. However, remember you will be tested on this material, so you need to show your work on each problem.