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## PowerPoint Slideshow about ' Warm-up. Wed. Jan 26' - kiora

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Presentation Transcript

Recall: To solve a quadratic equation like the following, use a square root method:

Goal for this lesson:

Radical equation such as:

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

3 a) Practice simplifying radicals

- Factor the number.
- Look for the greatest perfect square

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

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

4. Solving Equations with Roots

Solve the following equation.

5. Rationalizing Denominators

Goal: Remove radicals in the denominators

Key Idea:

For a denominator of the form

Multiply numerator and denominator by:

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,

6 b) Simplifying Fractional Exponents

Simplify the following expressions.

6 c) Practice simplifying radicals using rational exponents

Examples.

Rewrite each radical using rational exponents and simplify.

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.

8. Factoring Fractional Exponents

Factor out the GCF.

8. Factoring Fractional Exponents

Factor out the GCF.

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