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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:

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

cubed root of 8 is 2

Definition

The principal nthroot of a numberis defined as:

1)

2)

3)

Product Rule for nth Roots

Quotient Rule for nth Roots

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

1)

2)

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

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

Solve the following equation.

Goal: Remove radicals in the denominators

Key Idea:

For a denominator of the form

Multiply numerator and denominator by:

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,

Simplify the following expressions.

1)

2)

Simplify the following expressions.

Examples.

Rewrite each radical using rational exponents and simplify.

Solve the following formula for V:

Solve the following formula for A:

Simplify:

Method 1:

Look for powers of each term that match the root.

Method 2:

Rewrite using rational exponents and simplify.

1)

2)

3)

Factor out the GCF.

Factor out the GCF.