Powers, Roots and Radicals Review

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

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

Simplifying Radicals Practice Simplify the Expressions Answer Answer Home

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

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

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

Dividing Radicals Practice Divide the Expressions Answer Answer Multiply by Multiply by Home

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

Adding and Subtracting Radicals Practice Add or Subtract the Expressions Answer Answer Careful! and are NOT like terms! Simplify to first Home

Rational Exponents • Radicals can be re-written with exponents: • Use properties of exponents to simplify expressions when appropriate. Example 3: Example 2: Example 1: Practice Home

Rational Exponents Practice Simplify the Expressions Answer Answer Home

Solving Equations Solving Equations with Exponents Solving Equations with Radicals • Step 1: Isolate the power • Step 2: Take the nth root of both sides of the equation (where n is the exponent). • Step 3: Solve further if necessary. • [If the exponent is a fraction, just raise both sides of the equation to the reciprocal power] • Step 1: Isolate the power • Step 2: Raise both sides of the equation to the nth power (where n is the index of the radical). • Step 3: Solve further if necessary. Always check your answer! Practice Home

Solving Equations Practice Solve the Equations Answer Answer Don’t forget when taking the nth root and n is even! More Practice Home

More Solving Equations Practice Solve the Equations Answer Answer Get the radicals on opposite sides of the equation and square each side. After isolating raise each side to the power. Home

Powers, Roots and Radicals Review