Warm-up.  Wed. Jan 26
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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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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


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


1. nth Roots

cubed root of 8 is 2

Definition

The principal nthroot of a numberis defined as:


2. Evaluating nth Roots

1)

2)

3)


3. Properties of nth Roots

Product Rule for nth Roots

Quotient Rule for nth Roots


3 a) Practice simplifying radicals

  • Factor the number.

  • Look for the greatest perfect square


3 b) Multiplying and Combining Radicals

1)

2)


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 a) Simplifying Fractional Exponents

Simplify the following expressions.

1)

2)


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.


Day 2: Warm-up

Solve the following formula for V:

Solve the following formula for A:

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.


7 a) Simplify Radicals


7 b) Practice Simplifying Radicals

1)

2)


7 b) More practice Simplifying Radicals

3)


8. Factoring Fractional Exponents

Factor out the GCF.


8. Factoring Fractional Exponents

Factor out the GCF.


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