 Download Download Presentation # Powers, Roots and Radicals Review

Download Presentation ## Powers, Roots and Radicals Review

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1. Simplifying Radicals Explanation Adding and Subtracting Rational Exponents Click on a topic to review, then click practice for some problems! Practice Practice Practice Multiplying Radicals Dividing Radicals Explanation Powers, Roots and Radicals Review Solving Equations Practice Practice Practice

2. Simplifying Radicals Example: Simplify • Step 1: Put all numbers in prime factorization form (make a factor tree) • Step 2: Divide each exponent under the radical by the index. This will tell you what can be taken out of the radical and what is left. • Step 3: Simplify if necessary outside the radical and within the radicand. • Don’t forget absolute value if the index is even and a resulting power on the outside of the radical is odd. Show Step 1 Show Step 2 Show Step 3 Practice Home

4. Multiplying Radicals Practice • Step 1: Multiply the numbers/variables on the outside of the radical, and then multiply the numbers/variables on the inside of the radical. • Step 2: Simplify [See Simplifying Radicals for help] Example: Practice Home

5. Multiplying Radicals Practice Multiply the Expressions Answer Answer This is an example of multiplying conjugates. Remember, Home

6. Dividing Radicals A simplified answer can NEVER have a radical in the denominator. If there is, you must RATIONALIZE the denominator. One term in the denominator: Two terms in the denominator: • Step 1: Simplify all radicals. • Step 2: Multiply both numerator and denominator by the same radical. To find the appropriate radical, subtract the index from each exponent in the radicand of the denominator. • Step 3: Multiply and simplify. • Step 1: Simplify all radicals. • Step 2: Multiply both numerator and denominator by the conjugate of the denominator. • Step 3: Multiply and simplify. Example: Example: Practice Home

8. Adding and Subtracting Radicals • Step 1: Simplify all terms. • Step 2: Combine LIKE terms. Like terms have identical indices and radicands.Add or subtract the coefficients in front of the radicals and KEEP THE RADICAL PART THE SAME Example: Practice Home