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

Warm-up. Wed. Jan 26

Simplify Completely. No zero or negative exponents

1.

2.


Warm up wed jan 26

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

Review: Laws of Exponents


Warm up wed jan 26

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 n th roots

1. nth Roots

cubed root of 8 is 2

Definition

The principal nthroot of a numberis defined as:


2 evaluating n th roots

2. Evaluating nth Roots

1)

2)

3)


3 properties of n th roots

3. Properties of nth Roots

Product Rule for nth Roots

Quotient Rule for nth Roots


3 a practice simplifying radicals

3 a) Practice simplifying radicals

  • Factor the number.

  • Look for the greatest perfect square


3 b multiplying and combining radicals

3 b) Multiplying and Combining Radicals

1)

2)


4 solving radical equations

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

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 roots1

4. Solving Equations with Roots

Solve the following equation.


5 rationalizing denominators

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

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

6 a) Simplifying Fractional Exponents

Simplify the following expressions.

1)

2)


6 b simplifying fractional exponents

6 b) Simplifying Fractional Exponents

Simplify the following expressions.


6 c practice simplifying radicals using rational exponents

6 c) Practice simplifying radicals using rational exponents

Examples.

Rewrite each radical using rational exponents and simplify.


Day 2 warm up

Day 2: Warm-up

Solve the following formula for V:

Solve the following formula for A:

Simplify:


7 a simplify radicals 2 methods

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 a) Simplify Radicals


7 b practice simplifying radicals

7 b) Practice Simplifying Radicals

1)

2)


7 b more practice simplifying radicals

7 b) More practice Simplifying Radicals

3)


8 factoring fractional exponents

8. Factoring Fractional Exponents

Factor out the GCF.


8 factoring fractional exponents1

8. Factoring Fractional Exponents

Factor out the GCF.


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