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Warm-up. Wed. Jan 26

Warm-up. Wed. Jan 26. Simplify Completely. No zero or negative exponents 1. 2. Review. Recall: To solve a quadratic equation like the following, use a square root method:. Goal for this lesson: Radical equation such as:. Review: Laws of Exponents.

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Warm-up. Wed. Jan 26

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  1. Warm-up. Wed. Jan 26 Simplify Completely. No zero or negative exponents 1. 2.

  2. Review Recall: To solve a quadratic equation like the following, use a square root method: Goal for this lesson: Radical equation such as:

  3. Review: Laws of Exponents

  4. Section A.9 nth Roots; Rational Exponents; Radical Equations • nth Root • Evaluating nth roots • Properties of nth roots • Solving Radical Equations • Rationalize Denominators • Fractional Exponents • Simplifying Fractional Exponents • Simplifying radicals using rational exponents • Simplify radicals some more • 2 methods • More practice

  5. 1. nth Roots cubed root of 8 is 2 Definition The principal nthroot of a numberis defined as:

  6. 2. Evaluating nth Roots 1) 2) 3)

  7. 3. Properties of nth Roots Product Rule for nth Roots Quotient Rule for nth Roots

  8. 3 a) Practice simplifying radicals • Factor the number. • Look for the greatest perfect square

  9. 3 b) Multiplying and Combining Radicals 1) 2)

  10. 4. Solving Radical Equations Solve the following equation. Isolate radical to one side of equation Raise both sides to power equal to index of radicand Check for extraneous solutions

  11. 4. Solving Equations with Roots Solve the following equation. Isolate radical to one side of equation Raise both sides to power equal to index of radicand Check for extraneous solutions

  12. 4. Solving Equations with Roots Solve the following equation.

  13. 5. Rationalizing Denominators Goal: Remove radicals in the denominators Key Idea: For a denominator of the form  Multiply numerator and denominator by:

  14. 6. Fractional Exponents If a is a real number and is an integer, then If a is a real number and m and n are integers containing no common factors, with , then,

  15. 6 a) Simplifying Fractional Exponents Simplify the following expressions. 1) 2)

  16. 6 b) Simplifying Fractional Exponents Simplify the following expressions.

  17. 6 c) Practice simplifying radicals using rational exponents Examples. Rewrite each radical using rational exponents and simplify.

  18. Day 2: Warm-up Solve the following formula for V: Solve the following formula for A: Simplify:

  19. 7. a) Simplify Radicals – 2 methods Method 1: Look for powers of each term that match the root. Method 2: Rewrite using rational exponents and simplify.

  20. 7 a) Simplify Radicals

  21. 7 b) Practice Simplifying Radicals 1) 2)

  22. 7 b) More practice Simplifying Radicals 3)

  23. 8. Factoring Fractional Exponents Factor out the GCF.

  24. 8. Factoring Fractional Exponents Factor out the GCF.

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